离去的伦理

Two dated letters

In his May 25 letter to the IHÉS Scientific Committee, Grothendieck announced his decision and said departure would probably take effect October 1. In a June 9 letter to the director, he confirmed October 1 as effective. These one-page letters establish addressee, decision, and chronology; this account does not reconstruct a scene or quote their wording.11Grothendieck, Aux membres du Comité scientifique [de l’IHÉS]; Grothendieck, Letter to the director of the IHÉS confirming his departure.

The letter followed a documented sequence. On April 6, conflict over grants from the Ministry of the Armies had erupted in the scientific committee. A few days later, according to the board’s April 22 minutes, Grothendieck wrote that he would no longer participate in the committee. The board accepted the proposed 90,000-franc grant and prioritized its use for invitations of physicists. By late May the condition Grothendieck had stated—refusal of such funds if he were to remain—had not been met.22Institut des Hautes Études Scientifiques, Archives de l’IHÉS, minutes of the board meeting of April 22, 1970, A3.1.4.2.2/1.

Resignation was therefore a coherent enactment of a declared boundary. It was not ethically simple. Grothendieck did not leave a solitary office containing work that belonged only to him. He left an institute whose early scientific identity he had helped establish, a seminar community formed around his program, large bodies of unfinished redaction, students and colleagues working on questions he had proposed, and mathematical languages already used far beyond Bois-Marie.

The ethics of departure begin at that point. They concern what one person may require of an institution, what a teacher may expect of close collaborators, what happens to shared work after its central organizer withdraws, and which obligations accompany freely given ideas. A board vote cannot settle them. Their history begins in the forms of collaboration that preceded the break.

Four kinds of making

Mathematical publication often hides several kinds of work under one byline. For the Grothendieck school, at least four should be kept distinct.

The first is conceptual origination: identifying the right object, program, conjecture, or formalism. The second is mathematical construction: supplying definitions, proofs, examples, counterexamples, or extensions. The third is redaction: turning lectures, prenotes, or drafts into a coherent exposition with complete arguments and references. The fourth is editing and production: deciding organization, enforcing notation, typing, correcting, and preparing text for publication.

One person may perform all four. EGA and SGA repeatedly distributed them. Grothendieck supplied an extraordinary share of conceptual origin and mathematical construction; he also wrote extensive drafts and edited with minute attention. Dieudonné transformed drafts and contributed material. Students delivered exposés, solved assigned problems, and wrote chapters. Typists and publication staff converted manuscripts into stable pages. Treating only the first kind as authorship erases mathematics done in the others. Treating all kinds as identical erases the architecture that made the work cohere.

This distinction is not a modern correction imposed on an innocent past. The documents themselves preserve differentiated roles. EGA’s formula says Grothendieck “with the collaboration of Jean Dieudonné.” SGA title pages and tables of contents identify directors, editors, collaborators, and individual exposé authors. Hartshorne’s Residues and Duality states that it presents a seminar on Grothendieck’s work while naming Hartshorne as author. The bibliography is already an ethics of attribution, though not a complete one.

EGA: “with the collaboration”

The EGA formula has attracted contrary reductions. In one, Grothendieck wrote EGA and Dieudonné merely polished it. In another, the two were effectively equal coauthors obscured by hierarchy. The strongest evidence supports neither slogan. Grothendieck provided the global plan and elaborate drafts. Dieudonné rewrote, filled details, added complements, polished proofs, and contributed substantially to technically important sections.33Jackson, “As If Summoned from the Void, I,” 1050–51; Illusie and et al., “Reminiscences of Grothendieck and His School,” 10–11.

Armand Borel’s remembered contrast—that Grothendieck held the global vision while Dieudonné worked line by line—captures an asymmetry but can sound harsher than the result. Line-by-line control of eighteen hundred pages is not clerical labor. A foundational text fails if local arguments do not support its architecture. Illusie’s more detailed recollection credits Dieudonné with material concerning differential calculus in positive characteristic, complete local rings, and excellent rings. That is mathematical contribution.

The phrase “with the collaboration” should therefore be preserved rather than normalized into current journal practice. It recorded the project’s own account of roles. A biographer may explain why the phrase is insufficient for modern readers, but should not silently replace it.

EGA’s style makes collaboration unusually hard to see. The text speaks in an impersonal theorem-proof voice. Cross-references bind sections into one system. There is no diary of who supplied each lemma. The very success of the style—its appearance as one coherent architecture—absorbs the evidence of different hands.

Grothendieck’s 1967 instructions for manuscript preparation extend that absorption into material production. Typists were told exactly how to render underlining, formulas, punctuation, Greek letters, and EGA/SGA references. They were to consult authors about doubtful passages and not alter text without consent. The instruction sheet makes authority visible: the author’s text governs. It also makes dependence visible: authoritative text reaches print through skilled readers able to recognize notation and spot uncertainty.44Grothendieck, “Instructions générales sur la préparation des manuscrits,” 1–5.

No ethics of authorship can solve this by adding every typist to a title page. Attribution has forms other than coauthorship: acknowledgments, archive records, production histories, and narrative description. The obligation is not to pretend all labor is the same. It is to stop treating the labor that does not receive a theorem’s name as nonexistent.

Grothendieck later described exhaustive redaction as a form of service to the mathematical community. The claim has force. EGA made a new language available in a durable, searchable structure. It also served Grothendieck’s standards and authority. Service and self-expression need not be opposites. A public work can embody a powerful individual vision while enabling others.

SGA: a book made from voices

The SGA seminars began with speech and ended, often years later, in books. Grothendieck might prepare prenotes, assign a talk, listen to the exposition, and scrutinize a written draft. The expositor might fill gaps, reorganize material, or solve a new problem. Other participants might ask questions that changed the final proof. An editor might later reconcile notation across the volume. The published exposé was an endpoint of this chain, not a transcript in the narrow sense.

Illusie’s first assignments show the apprenticeship. He entered with little algebraic geometry, was asked to write notes, and returned to Grothendieck’s home for long revision sessions. He remembered his pages covered in pencil. The corrections addressed mathematics, French, punctuation, and organization. The standard was that every assertion be proved or referenced; phrases such as “it is clear” were suspect.55Illusie and et al., “Reminiscences of Grothendieck and His School,” 1–3; Artin et al., “Alexandre Grothendieck 1928–2014, Part 1,” 252–53.

This practice could produce authors rather than copyists. Illusie later recalled proposing a more general fibered setting in SGA 6 and described Berthelot’s work on a K-theoretic problem. The final volume bears Berthelot’s, Grothendieck’s, and Illusie’s names. The recollection supplies process; the title page supplies formal authorship.66Berthelot et al., Théorie des intersections et théorème de Riemann–Roch (SGA 6); Illusie and et al., “Reminiscences of Grothendieck and His School,” 3–4.

SGA 7 supplies further distinctions. Illusie later recalled Grothendieck asking Deligne to treat Picard–Lefschetz theory in étale cohomology, while Katz later recalled receiving Lefschetz pencils as a subject. The published volumes preserve their exposé bylines. The A2 accounts describe assignment and process; the volumes identify formal authorship.77Grothendieck, Groupes de monodromie en géométrie algébrique (SGA 7 I); Deligne and Katz, Groupes de monodromie en géométrie algébrique (SGA 7 II); Illusie and et al., “Reminiscences of Grothendieck and His School”; Artin et al., “Alexandre Grothendieck 1928–2014, Part 1”.

Official posters strengthen the point. In March and November 1968, IHÉS announced the local-monodromy seminar as directed by “P. Deligne et A. Grothendieck.” The younger mathematician’s shared directorship was public before the institutional breach. Describing Deligne only as a pupil who inherited the work after 1970 would erase that documented authority.88Institut des Hautes Études Scientifiques, Archives de l’IHÉS, poster, “Groupes de monodromie locale,” March 5, 1968, J6.1.8/2; Institut des Hautes Études Scientifiques, Archives de l’IHÉS, poster, “Groupes de monodromie locale (suite),” November 19, 1968, J6.1.8/1.

A 1970 IHÉS inventory offers an almost forensic counterweight to the collective label. It lists 184 pages on presheaves under Grothendieck and Jean-Louis Verdier; 210 pages of an SGA 4 exposé under Deligne; 73 pages on the cohomological study of Lefschetz pencils under Katz; and 97 pages on finiteness conditions, topoi, fibered sites, and limits under Grothendieck and Verdier. The page counts do not measure originality. They do prove that the institution could name work at a finer resolution than “Grothendieck’s school.”99Institut des Hautes Études Scientifiques, Archives de l’IHÉS, “Travaux de mathématiques et de physique théorique, année 1970,” F3.2.2.1/4, pp. 1–2.

The inventory is an institutional production record rather than a contribution statement. Its bylines and page counts are direct evidence for listed texts, but they do not reveal who proposed each lemma, revised each proof, or resolved each objection. Later testimony can illuminate process only with visible attribution.1010Institut des Hautes Études Scientifiques, Archives de l’IHÉS, “Travaux de mathématiques et de physique théorique, année 1970,” F3.2.2.1/4.

This difference between inventory and intellectual genealogy is central to the chapter: recoverable names prevent erasure, while the record’s silence prevents invented allocations of credit.

The delayed publication of seminar volumes complicated the record. An exposé delivered in the 1960s might appear in a Springer volume years later. Authors could revise, editors could intervene, and the field could change before the book arrived. A citation to the publication year alone may misdate the mathematics; a citation to the seminar year alone may ignore later redaction. This biography will give both where they matter.

Delay also increased ethical risk. Memories of origin diverge. A result that circulated in notes may become associated with the person who gave the clearest published proof. A program’s director may see the result as a branch of his vision; the expositor may remember the difficult work that made it true. Bibliography can identify the final text without fully resolving intellectual genealogy.

Giving problems

Witnesses repeatedly describe Grothendieck’s generosity with problems and ideas. Katz remembered that being asked to join a task felt like an honor and that Grothendieck had an uncanny ability to match subjects to people. Hartshorne received pages of further questions after sending a thesis. Visitors left with programs that shaped careers.1111Jackson, “As If Summoned from the Void, I,” 1053–55; Artin et al., “Alexandre Grothendieck 1928–2014, Part 1,” 251–54.

The gift metaphor is apt and incomplete. A problem given to a young mathematician can be enabling: it opens terrain and conveys confidence. It can also place the recipient inside the giver’s architecture, where success will be interpreted as a realization of the program. The recipient gains an opportunity and inherits a relation.

No single rule determines the resulting credit. If Grothendieck stated a theorem and another person proved it, both roles should be named. If he suggested an area and the recipient found an unexpected theorem, the recipient’s originality should not be reduced to execution. If a student wrote an exposé from detailed prenotes, the written byline and source of the notes both matter. Ethical history is grammatical before it is judicial.

The field’s conventions were less formalized than current contribution statements. Papers did not list conceptualization, methodology, writing, supervision, and funding in a standardized taxonomy. Seminar culture relied on shared understanding. Such understanding works while a community remains close. It becomes fragile after people separate and readers encounter only printed remnants.

Grothendieck’s authority intensified the fragility. His ideas became so pervasive that later papers sometimes used them without repeating his name. Serre later argued that everyone knew where motives or $\ell$-adic cohomology came from, so the absence of a citation did not assign the ideas to someone else. That defense reflects a community in which tacit knowledge carried attribution. It also reveals why someone outside or later than the community might not see the debt.1212Jackson, “As If Summoned from the Void, II,” 1208–9.

Modern citation practice tends to prefer explicitness, but explicit citation cannot be mechanically retrofitted. The task is to record what contemporaries knew, what texts said, and how conventions changed. A missing footnote may represent appropriation, ubiquity, carelessness, or a different norm. Motive cannot be inferred from absence alone.

Generosity and severity

The seminar’s generosity coexisted with severity. Some students found Grothendieck’s detailed criticism intolerable. Thom felt the dominance of the school diminished space for his own mathematics. Cartier remembered political tactics that alienated people who shared Grothendieck’s goals. These testimonies cannot be averaged into a personality score. They identify effects that differed by relation and context.

Grothendieck’s pedagogical patience also has multiple witnesses. Deligne recalled that a basic question received a gentle answer without condescension. Illusie remembered lectures that supplied prerequisites clearly enough for a newcomer to grasp the formal structure. The teacher who blackened a draft could take care to make a lecture accessible.

Contradiction is not a defect in the record. A person can be patient with ignorance and impatient with imprecision. A leader can give ideas freely and dominate an intellectual environment. A collaborator can welcome original contributions and still reserve final editorial authority. The ethics lie partly in how those combinations affect others, not in selecting one adjective as the true one.

Later biography has sometimes used childhood exile or anarchist inheritance to explain every uncompromising act. Such explanations exceed evidence and turn life history into destiny. Grothendieck’s past is relevant where he invoked it or where actions establish a durable commitment. It does not decode each interaction at the seminar table.

The same restraint applies to “charisma.” Named witnesses use the concept to describe why people accepted difficult tasks. Charisma is an observed social force, not an occult property. It consisted in mathematical authority, intensity, attention, generosity, and the belief that the program mattered. Its ethical ambiguity comes from its effectiveness: people could act freely and still find their choices powerfully shaped.

The retrospective indictment

More than a decade after leaving IHÉS, Grothendieck wrote Récoltes et Semailles. Parts of the work accused former students and colleagues of failing to credit, publish, or continue his ideas and of participating in what he called a burial of his work and person. The accusations are historically important. They are also retrospective, extensive, and contested.1313Grothendieck, Récoltes et Semailles (Université des Sciences et Techniques du Languedoc and Centre National de la Recherche Scientifique, 1986); Jackson, “As If Summoned from the Void, II,” 1206–9.

They cannot be imported into May 1970 as hidden reasons for resignation. The chronology runs the other way. The military-funding conflict produced the institutional break. Later mathematical developments and publications contributed to the grievances articulated in the 1980s. To say that he left because students would bury his work would invent foreknowledge.

The accusations also cannot be dismissed by noting their later date. They contain recollections of the seminar, explicit ethical arguments, and information about manuscripts and transmission. Herreman’s study takes them seriously as a text about collective mathematics while expressly refusing to verify every claim about the people named. That methodological warning should govern this biography. Récoltes et Semailles is primary evidence for Grothendieck’s judgment and self-understanding; it is not independent proof of its charges.1414Herreman, Découvrir et transmettre: La dimension collective des mathématiques dans *Récoltes et Semailles* d’Alexandre Grothendieck, introduction.

Serre’s response, as reported by Jackson, distinguished inadequate explicit credit from deliberate appropriation. Grothendieck’s influence was so pervasive that mathematicians often did not repeat his name, but, Serre argued, no one thereby claimed the ideas as someone else’s. He also contrasted the accusations with Grothendieck’s earlier generosity. This is a substantive response, not a final verdict.

Illusie rejected the idea that Grothendieck had been deliberately buried, pointing to the ubiquity of his language and methods. At the same time, shifts in research after 1970 were real. Mathematicians combined general theory with more specific problems; some paths Grothendieck valued were not pursued in the way he expected. A program can remain foundational while its founder experiences the community’s choices as abandonment.

The phrase “burial” fuses credit, continuation, and personal relation. They should be separated. A paper may cite an idea inadequately. A student may choose not to develop a suggested chantier. An editor may delay a volume. A field may alter style. A friend may cease contact. Each can wound; they are not the same ethical act.

This separation also protects former students from an impossible obligation. Receiving a problem does not place one’s career in permanent service to the giver. Intellectual gratitude can require acknowledgment and honesty. It cannot require identical priorities for life. Grothendieck’s later expectation that certain people should have continued particular programs was one claim about apprenticeship, not a generally binding rule.

The request to leave together

Jackson reports that after the funding conflict Grothendieck tried to persuade the other permanent professors to resign with him. None did. Pierre Deligne, recently appointed and mathematically close to Grothendieck, also declined. Deligne later remembered that Grothendieck was surprised and deeply disappointed that their closeness in mathematics did not extend to the nonmathematical decision.1515Jackson, “As If Summoned from the Void, II,” 1198.

In Deligne’s recollection, Grothendieck’s surprise and disappointment concerned the fact that mathematical closeness did not produce the same institutional decision. The account supports that bounded contrast and no further private motive.1616Jackson, “As If Summoned from the Void, II,” 1198.

A call for collective resignation can be ethically powerful. If every permanent professor leaves, an institution must confront the disputed policy. A lone resignation risks symbolic isolation. Solidarity gives moral protest material consequence. Grothendieck’s effort to recruit colleagues was therefore not inherently coercive.

Power changes its texture. A senior figure who has shaped a younger colleague’s appointment and program asks for an act that may end the colleague’s new institutional position. The younger colleague’s refusal protects moral and professional independence. Mathematical gratitude does not entail political obedience. Deligne’s decision is especially important because later narratives often cast him as heir. An heir is not a delegate.

The other professors faced their own obligations. Michel and Ruelle had already proposed a compromise. They may have judged the grant acceptable under conditions, the tactics ineffective, or the institute worth preserving despite disagreement. The sources do not permit one motive to be assigned to all. “They refused to resign” is firm. “They chose money over conscience” is polemic, not history.

Grothendieck’s disappointment is equally human without being a command the narrative must endorse. People working intensely together often overestimate the transferability of agreement. The seminar had demonstrated deep convergence on what counted as a natural mathematical question. Institutional ethics did not possess the same proofs or shared axioms.

This difference may have been difficult precisely because Grothendieck’s mathematics sought coherence. In a well-formed category, maps and compatibilities organize many objects. A community is not a category in that technical sense. Personal, political, financial, and professional obligations do not compose according to one formal law. The analogy can illuminate an expectation and must stop before it judges.

Custody of the unfinished pages

Departure redistributed practical responsibilities. Seminar notes still needed completion. Manuscripts circulated in partial form. Publishers and editors needed decisions. Students needed supervision or new institutional anchors. The mathematical questions did not resign.

The 1970 IHÉS inventory is evidence of texts in progress during rupture. It records entries under Grothendieck’s name, joint entries with Verdier, and entries under Deligne and Katz. The list does not measure originality, establish readiness for publication, or assign later editorial responsibility.1717Institut des Hautes Études Scientifiques, Archives de l’IHÉS, “Travaux de mathématiques et de physique théorique, année 1970,” F3.2.2.1/4.

When a director of a program leaves, several editorial models are possible. One is custodial: collaborators preserve and publish the material with minimal alteration. Another is developmental: they revise it in light of new results. A third is selective: they publish some material and let other projects lapse. In his later criticism, Grothendieck argued that specified construction sites should have been continued; former students and colleagues made different choices.1818Grothendieck, Récoltes et Semailles (Université des Sciences et Techniques du Languedoc and Centre National de la Recherche Scientifique, 1986); Jackson, “As If Summoned from the Void, II,” 1207–9.

No model is automatically right. Fidelity can freeze an unfinished thought and consume years. Development can obscure origin. Selection can look like burial to the person whose priorities are rejected. The obligations depend on explicit agreements, bylines, the completeness of manuscripts, and the needs of readers. This is why primary contracts and correspondence matter.

SGA’s eventual publication history contains examples of all three models. Some volumes appeared after long redaction. Some material was reorganized. Some plans remained incomplete. The collective did not vanish with Grothendieck’s departure, but it changed from a group organized by his current direction to a diaspora interpreting inherited work.

The word inheritance can itself mislead. Mathematics is not an estate over which one person has testamentary control. Ideas become available for proof, correction, and use. Yet manuscripts, attribution, and editorial decisions create concrete responsibilities. One may reject proprietary ownership without accepting amnesia.

The ethical minimum is recoverability: preserve who said what when, retain individual bylines, identify prenotes, distinguish seminar year from publication year, and mark later revisions. The archive makes such recoverability possible.

Service without possession

In Récoltes et Semailles, Grothendieck later presented mathematics as a collective undertaking whose meaning exceeded any one participant. This claim is known here through Herreman’s transcription and remains unverified against the primary French text. It describes Grothendieck’s later interpretation and must not be projected backward as a motto already governing the seminar.1919Herreman, Découvrir et transmettre: La dimension collective des mathématiques dans *Récoltes et Semailles* d’Alexandre Grothendieck, 1, citing Récoltes et Semailles, p. 1234.

His earlier practice nevertheless contained a strong ethic of service. He wrote long foundations so others could work safely. He explained prerequisites. He gave problems. He opened his home for revision and discussion. He treated naming as part of discovery and tried to place ideas in natural frameworks. These are evidenced acts, not a claim of moral perfection.

Service can become possessive when the server expects beneficiaries to remain within his design. Possession can masquerade as service when one claims authority because one has given much. Conversely, recipients can invoke the collective to erase originators. The Grothendieck story contains anxieties on both sides.

The fairest account does not search for a point at which generosity turned into grievance, as though one essence replaced another. In the 1960s, generosity and authority were simultaneous. In the 1980s, affirmation of collective mathematics and anger at former collaborators were simultaneous in Grothendieck’s retrospective account.

This complexity also belongs to authorship. Grothendieck could originate the motivic program without authoring Manin’s paper. Dieudonné’s documented EGA role differs from Grothendieck’s. Deligne’s later Weil proof and Katz’s exposés retain their own authorship even where Grothendieck proposed a program or subject. Precise verbs can preserve these relations without assigning one owner to the entire field.

Resigning alone

The May 25 decision made Grothendieck’s stated boundary personal. He could not compel IHÉS to refuse the grant, but he could set an effective date for leaving his position. His letter of June 9 fixes that date at October 1.2020Grothendieck, Aux membres du Comité scientifique [de l’IHÉS]; Grothendieck, Letter to the director of the IHÉS confirming his departure.

The act did not release him from every consequence. Students and texts remained. Nor did it oblige him to continue managing an institution whose funding he rejected. A person may leave a collective project even when departure burdens others. The ethical question is whether commitments are acknowledged and transitioned, not whether leaving is forbidden.

The letters do not establish what arrangements Grothendieck proposed for students, offices, manuscripts, or seminar records. Other sources document continued mathematical lectures and public interventions during the interval before October 1.

Calling the chapter “The Ethics of Departure” should not imply that Grothendieck wrote a systematic ethic in May. The ethics emerge from acts and disagreements: his refusal, the board’s vote, colleagues’ decisions, the distributed authorship of unfinished work, and later arguments about memory.

No collective resignation followed. IHÉS continued. Deligne remained and did mathematics central to the future of the field. Grothendieck left and soon helped create Survivre. Both paths would be judged through the lens of the relationship that had preceded them.

The door did not close on mathematics at the date of the letter. In July, Grothendieck would lecture for hours on motives in Montréal and teach Barsotti–Tate groups. The institutional departure was sharp; intellectual departure was not. That distinction is the point from which the final chapter of this Part must begin.

Hartshorne: a book between names

Robin Hartshorne’s Residues and Duality offers a microhistory of attribution. Grothendieck had announced a duality program but did not make it the subject of his current IHÉS seminar. Hartshorne offered a Harvard seminar. Grothendieck sent roughly 250 pages of prenotes. Hartshorne digested them, filled details, lectured, reorganized the material, and circulated drafts back for correction.

The published volume appeared in 1966 as Lecture Notes in Mathematics 20. Its title page described lecture notes of a seminar on the work of A. Grothendieck and named Hartshorne as author, with an appendix by Deligne. That formula is more exact than either “Grothendieck’s duality book” or “Hartshorne independently wrote duality.” It gives the reader a genealogy.

Hartshorne later remembered repeated returns covered in red ink. Eventually he sent the book to the publisher because revision could have continued indefinitely. The decision marks a real authorial boundary. An editor can always imagine improvement; an author must decide when a text can leave the relation.

The episode shows that control and gratitude need not align perfectly. Hartshorne regarded the period as an apprenticeship and credited Grothendieck’s material. He also made the practical decision to publish without waiting for an unreachable final state. The book’s usefulness depended on both fidelity and closure.

Its appendix by Deligne adds another layer. A volume can contain a main exposition written from one mathematician’s prenotes and a separate contribution by another. Bibliographic granularity lets readers assign credit without treating the object as fragmented.

This model differs from EGA. Hartshorne’s name occupies the author position, while Grothendieck’s appears as the mathematician whose theory is presented. The difference reflects genre and decision, not a simple measure of how many original ideas each supplied.

It also differs from SGA, where the seminar’s own acronym and exposé structure became the bibliographic identity. A responsible biography must preserve these genre-specific formulas. There was no single “Grothendieck school authorship practice.”

Illusie and Berthelot: an assignment becomes research

Illusie entered Grothendieck’s seminar through a question about an index formula in a relative setting. Grothendieck redirected the question toward ringed spaces, pseudocoherent complexes, and finite Tor dimension. The initial intervention overwhelmed the younger mathematician but later proved useful. This is conceptual supervision at its strongest: the adviser sees a framework the student cannot yet command.

When Grothendieck assigned Illusie notes on local duality and later work in SGA 6, redaction taught the framework. The act of writing exposed what the student did not know and what the prenotes had not specified. Revision was not post-production. It was part of learning and sometimes part of discovery.

Illusie later recalled proposing a fibered-category generalization in SGA 6 and described his own initial uncertainty. This is evidence about process, not a transcript of the seminar.2121Illusie and et al., “Reminiscences of Grothendieck and His School,” 3–4.

In the same recollection, Illusie described Berthelot adapting constructions from EGA II to complexes for a projective-bundle problem and reported Grothendieck’s praise of the treatment. The chapter presents this as Illusie’s technical memory.2222Illusie and et al., “Reminiscences of Grothendieck and His School,” 3–4.

The humor matters only because the mathematics is identifiable. Praise from a master does not create Berthelot’s authorship; the construction does. The byline and later testimony reinforce one another.

These examples complicate the phrase “students carried out Grothendieck’s program.” Carrying out may mean filling a known proof, finding a missing theorem, generalizing a framework, or inventing new methods. The phrase is acceptable only when followed by the particular act.

They also show why later claims of ownership can become painful. From Grothendieck’s viewpoint, the questions belonged to a coherent vision he had supplied. From a student’s viewpoint, the months spent making an idea true created a legitimate sense of authorship. Both are grounded in work.

An ethical history need not apportion a percentage. It can name the program, question, construction, proof, and text. Precision dissolves some zero-sum conflict.

Deligne and Katz: inheritance before departure

Deligne’s presence in the story is often organized around succession: Grothendieck leaves, Deligne proves Weil. The posters and recollections show an earlier, denser relation. Deligne attended from 1965, wrote SGA exposés from Grothendieck’s notes, asked elementary questions, supplied results, and jointly directed the local-monodromy seminar by 1968.

Grothendieck asked him to give an étale form of the Picard–Lefschetz formula. Deligne’s treatment later became important to the Weil proof. The sequence is an ideal case of collaborative genealogy: a question and context from Grothendieck, a mathematical construction by Deligne, later use in Deligne’s own architecture.

Calling Deligne an “heir” captures continuity and risks passivity. He inherited languages and problems, not a completed proof or an obligation to remain within every plan. His refusal to resign in 1970 is one institutional expression of that independence; his later mathematics is the stronger expression.

Katz’s Lefschetz-pencil work follows a parallel but distinct path. Grothendieck proposed a subject Katz barely knew. The assignment became seminar lectures and a long research trajectory. Here the originator’s judgment lay partly in selecting the person. Katz’s authorship lay in learning, proving, and writing.

The two cases reveal a central property of the seminar: it converted asymmetry into new centers of expertise. A successful adviser does not retain monopoly over a subject. The student becomes someone whose later judgment can diverge.

This development was visible before the breach. Joint directorship on a poster establishes that Deligne’s role already extended beyond receipt of Grothendieck’s ideas. Katz’s named exposés are bibliographic evidence of his authority. The school had already pluralized.

That pluralization helps explain why a collective resignation was unlikely. Permanent and visiting mathematicians had careers, programs, and institutional commitments increasingly their own. Grothendieck’s moral authority remained strong; it no longer defined one will.

Redaction as discovery

Herreman’s analysis of Récoltes et Semailles distinguishes author and redactor while showing how Grothendieck complicated the distinction. In his account, writing could be a way of listening to mathematics, not just reporting a result already present. An exposition might discover the natural order and therefore alter the content.

This view makes redaction intellectually serious. If a theorem cannot be stated cleanly without new definitions, the writer discovers structure. If a compatibility fails during exposition, the writer finds a missing condition. If two proofs become instances of one proposition, organization produces generality.

It also makes attribution harder. A speaker may supply the central idea while the redactor creates the form in which the idea becomes true and usable. Current conventions may name both authors. SGA often used the exposé byline and editorial apparatus. EGA used a collaboration formula.

There is no ethical gain in calling every editorial intervention discovery. Correcting punctuation is not proving a lemma. The four-kind distinction from this chapter remains necessary. Redaction becomes discovery when it changes mathematical understanding, and the evidence should identify how.

Grothendieck’s close correction reflected his belief that form and content were connected. A careless phrase could hide an unproved claim. An omitted compatibility could break later use. The severity was not mere stylistic control, although recipients could experience it as control.

His instruction that no assertion be false sounds minimal and becomes demanding in homological algebra, where signs and functorial compatibilities proliferate. Complete proof was a service to future readers who could not ask the seminar. It was also one reason volumes grew and publication slowed.

After departure, redaction lost its central arbiter. Editors had to decide how much generality, proof, and cross-reference would count as faithful. Differences could be interpreted as practical judgment or abandonment. The ethics of unfinished texts is inseparable from the epistemology of redaction.

A vocabulary for credit

This biography adopts a controlled vocabulary to avoid generic praise.

Introduced means a source shows a mathematician first defining or naming an object in the relevant context. It does not claim no precursor.

Formulated means a conjecture or program was stated in a recognizable form. Grothendieck formulated the standard conjectures; Kleiman expounded their formalism.

Proved belongs to the person or people supplying a proof, with hypotheses and date. If a seminar director proposed the theorem, that is separately named.

Developed requires an object specifying the part and construction. Used alone, it obscures.

Directed identifies institutional or editorial leadership. It does not assign every theorem in a seminar.

Redacted means turned lectures, notes, or drafts into written exposition, possibly with mathematical contribution specified separately.

With the collaboration of preserves a historical title-page formula and is followed by evidence about labor.

School names a network of training and shared program, not collective authorship.

This lexical discipline may seem bureaucratic in narrative prose. It is the minimum needed for a life whose work entered common language through many hands. Repetition of “Grothendieck created” would produce false grandeur by grammar alone.

Credit also requires negative discipline. Do not call a result “Grothendieck’s” merely because it appears in SGA. Do not remove his role because another person wrote the exposé. Do not call a student’s proof “just carrying out.” Do not infer theft from missing citation without evidence of source and convention.

A claim matrix can make these rules recoverable. Literary smoothness comes after attribution, not before.

Three dates for one exposé

An SGA exposé can carry at least three dates: the seminar talk, the written draft, and the eventual publication. These dates may be separated by years. A historical account that gives only the Springer volume date can make a 1960s result appear to belong to the 1970s; an account that gives only the lecture date can hide extensive later redaction.

The distinction affects credit as well as chronology. The speaker may have worked from Grothendieck’s prenotes. The written version may include arguments developed after questions from the seminar. A later editor may reconcile notation, add references, or incorporate corrections. The final byline remains essential, but it does not describe every stage by itself.

SGA 7 supplies a clear case. The seminar work took place in 1967–1969, while the two published volumes appeared in 1972 and 1973. The posters document joint direction for phases of the seminar. The tables of contents document individual exposés. Later testimony describes assignments and revision. No one source replaces the others.2323Grothendieck, Groupes de monodromie en géométrie algébrique (SGA 7 I); Deligne and Katz, Groupes de monodromie en géométrie algébrique (SGA 7 II); Institut des Hautes Études Scientifiques, Archives de l’IHÉS, poster, “Groupes de monodromie locale,” March 5, 1968, J6.1.8/2; Institut des Hautes Études Scientifiques, Archives de l’IHÉS, poster, “Groupes de monodromie locale (suite),” November 19, 1968, J6.1.8/1; Illusie and et al., “Reminiscences of Grothendieck and His School”; Artin et al., “Alexandre Grothendieck 1928–2014, Part 1”; Artin et al., “Alexandre Grothendieck 1928–2014, Part 2”.

This layered chronology also changes the meaning of “after Grothendieck.” A volume published after his resignation can contain work planned, spoken, or drafted before it. Its publication does not prove that former collaborators independently originated every part after 1970, and its earlier seminar date does not make every later editorial act his.

The ethical minimum is to name the stage under discussion. Grothendieck could originate a program and prepare notes; Deligne or Katz could prove and present an exposé; later editors could produce the volume readers use. Each verb carries a separate date and source.

Delayed publication also created practical responsibility after resignation. Someone had to preserve manuscripts, settle variants, correspond with authors, and decide when a text was ready. Those tasks were neither automatic custodianship nor permission to erase earlier contributors. They required judgment in a community whose central working relationship had changed.

The 1970 IHÉS inventory captures material in motion. Its entries and page counts show that substantial texts existed, but an inventory does not say that each was final. It cannot identify which revisions occurred after the report or why publication took a particular form.

Later disputes about neglect or appropriation must therefore be tested object by object. A delayed volume, an uncited oral suggestion, and an abandoned plan are different claims. A general narrative of burial cannot settle them collectively, and a general statement about Grothendieck’s ubiquity cannot answer every local question.

This stage-based method also avoids assigning moral intention from bibliographic delay. Publication can be slowed by incomplete proofs, incompatible notation, editorial standards, competing obligations, or conflict. Motive requires evidence beyond the elapsed years.

The distinctions are recorded here because prose compresses them easily. “Grothendieck’s seminar” is allowed as an institutional label; mathematical authorship follows the exposé and contribution record. “Published after his departure” is a date, not a verdict.

Departure and the duty to communicate

May 25 was a decision date, not the effective end of the appointment. The June 9 confirmation and October 1 date leave an interval in which lectures, correspondence, and editorial work continued.

The duty of an adviser leaving an institution can include informing students, arranging supervision, transferring notes, and clarifying publication. The available record is not sufficient to judge each duty. Later outcomes—theses completed, volumes published, relations damaged—cannot substitute for the missing transition correspondence.

The gap matters because moral narrative rushes to judgment. Grothendieck’s later accusations encourage a story in which he was abandoned. Former students’ shock encourages a story in which he abandoned them. Both may describe experiences. Neither can be converted into a complete 1970 ledger without documents.

The collective nature of mathematics distributes exit costs unevenly. A permanent professor can resign on principle and find another platform. A student may depend on an adviser’s signature or problem. An editor may inherit hundreds of pages. A visitor may lose a planned seminar. The principled act remains principled and has consequences.

Institutions can reduce those costs through transition procedures. The April minutes focus on contract and funding, not students or manuscripts. Perhaps other records do; they remain to find. Their absence from the board agenda may reflect institutional compartmentalization.

Grothendieck’s demand that colleagues resign created another communication duty: explain why this action, rather than internal opposition, earmarking, or later phase-out, was required. Jackson records disappointment but not the full arguments exchanged. A biography cannot supply them.

Deligne’s refusal states a boundary as legitimate as resignation. He could receive ideas, appointment support, and training without surrendering political judgment. The ethics of mentorship requires that possibility. Otherwise a gift becomes debt enforceable by loyalty.

Grothendieck’s own resignation also asserted independence from institutional debt. Motchane and IHÉS had made his work possible; that did not purchase future consent. The symmetry is important. Neither benefactor nor mentor owns the recipient.

Authorship after separation

While Grothendieck directed the seminar, uncertainty about a draft could return to him through a meeting, letter, or marked page. After resignation, the same question became an editorial decision among people who no longer shared the weekly working arrangement. Separation changed process before it changed attribution.

A manuscript might contain a detailed Grothendieck prenote, a student’s exposition, corrections from several readers, and later editorial work. Publication required identifying a responsible text even when intellectual origin remained distributed. The SGA byline system preserved more of this distribution than a single-author monograph, but it did not record every intervention.

Custody and authorship should therefore remain distinct. Possessing a manuscript does not make the custodian its mathematical author. Preparing it for publication can involve original work that deserves explicit credit. Refusing publication can arise from incompleteness rather than hostility. Each proposition requires a document.

The departure also changed the ethics of consent. An author present during revision can approve changes. An absent or disengaged originator may be difficult to consult. Editors must then distinguish correction, completion, and alteration. The available record does not provide a general authorization from Grothendieck covering every later volume.

Former students had independent obligations to readers. A seminar text that circulated in unstable copies could benefit from a reliable edition. Fidelity to the originator did not require preserving errors or obsolete organization. At the same time, modernization could obscure which language and proof belonged to the original period.

Date labels help preserve that distinction. A note can state that a lecture was delivered in 1968, redacted later, and published in 1973. A preface can identify changes. A byline can distinguish the expositor from seminar directors. These are documentary practices rather than solutions to every priority dispute.

Grothendieck’s later accusations treated some editorial and research choices as part of a wider moral decline. Former students answered from a different record of ubiquitous influence and continuing mathematics. Both positions are retrospective. Claims about a particular exposé still require its draft history, correspondence, and publication record.

The historian cannot settle local disputes by praising generosity or invoking hierarchy in general. Generosity establishes that ideas circulated. Hierarchy establishes unequal authority. Neither proves who wrote a proof or why a citation was omitted.

Separation also allowed styles to diverge. Some former students combined Grothendieck’s general language with detailed study of examples and specific problems. That shift can be described through publications. It should not be treated as betrayal of an essence or proof that the earlier program had been rejected wholesale.

The enduring ethical requirement is recoverable genealogy. Readers should be able to identify the originating program, the speaker or writer, the proof, the editor, and the publication date where sources permit. Gaps should remain gaps rather than being filled by the most famous name.

This requirement applies equally to Grothendieck’s claims. His originative role does not transfer authorship of later theorems. Later originality does not erase the program that made a question visible. The history is additive only when the additions remain named.

Departure made this naming harder because common understanding could no longer do silent work. It also made explicit records more important. The archive, title page, preface, and correspondence became the means by which a dispersed community could preserve relations once maintained in person.

Memory after common work

When a close collaboration ends, later memory often reallocates causality. The originator remembers giving the decisive idea. The writer remembers making it intelligible. The prover remembers the obstacle no one else crossed. The institution remembers providing conditions. All can be accurate at their own scale.

Récoltes et Semailles examines these scales at length and in moral terms. Its power does not remove its positionality. Grothendieck wrote as originator, former adviser, departed member, and critical interpreter of later mathematics.

Serre’s and Illusie’s responses are positional too. They remained inside or close to the mathematical community Grothendieck judged. Their insistence on his ubiquitous influence answers the claim of burial at the level of use. It may not answer every complaint about a citation, manuscript, or relationship.

The term “deliberate burial” is especially demanding. It attributes coordinated intent. Ubiquitous use weighs strongly against successful erasure; it does not logically disprove every act of marginalization. Each allegation would require its own evidence. This chapter refuses a collective verdict.

The 1960s record provides a counterweight without an acquittal. It shows explicit bylines, generosity, shared direction, and original student work. It also shows hierarchy and the absorption of labor into unified texts. Those conditions could support later misunderstandings without proving conspiracy.

The fairest memory is additive. Grothendieck’s architecture, Dieudonné’s redaction and mathematics, Deligne’s formulas and proof, Katz’s pencils, Illusie’s derived and deformation work, Berthelot’s complexes, Verdier’s categories, and the unnamed production labor all enter. Addition does not diminish the largest term.

The form of an ethical ending

An ethical ending to common work is rarely unanimous. One participant may require a public break; another may preserve the institution and change it from within; a third may continue the mathematics elsewhere. History should not force their decisions into one moral theorem.

Grothendieck’s resignation had integrity because it accepted personal cost after his condition failed. It also placed pressure on colleagues whose costs and judgments differed. The board exercised legal authority and preserved the institute. It also accepted a source one foundational professor regarded as disqualifying.

No later success cancels that disagreement. IHÉS’s flourishing does not prove its 1970 choice ethically right. Grothendieck’s later influence on ecological thought does not prove every tactic effective. Deligne’s proof of Weil does not retroactively justify staying, nor does the funding provenance taint his mathematics.

The ethical record consists in accountable reasons and consequences, not providential outcomes.

For authorship, the parallel standard is accountable genealogy. A theorem’s later importance does not determine who deserves credit. Documents, proofs, and labor do.

At the end of May, the board decision and Grothendieck’s written response were both visible, while October 1 remained the effective date. The collective mathematical record remained distributed across volumes still in progress.

The door closed with no final statement agreed by all sides. That incompletion is not a flaw the biographer should repair. It is the ethical form of the departure.

Six objects, six credit forms

The contribution problem becomes concrete when placed beside six objects.

EGA IV carries Grothendieck’s name with Dieudonné’s collaboration. Its unit is the treatise chapter, integrated into a single voice. Credit must explain vision, draft, revision, and substantive complements.

SGA 6 carries Berthelot, Grothendieck, and Illusie in the bibliographic record. Its unit is both seminar and exposé. Credit must preserve program and original solutions.

SGA 7 divides across volumes and bylines. Posters show joint direction by Deligne and Grothendieck for a phase; exposés identify Katz, Deligne, and others. Credit must be finer than the seminar title.

Residues and Duality names Hartshorne as author of notes on Grothendieck’s work, with a Deligne appendix. Credit is genealogical on the title page.

The standard conjectures paper names Grothendieck as author; Kleiman’s separate exposition names its own author and specifies contributions by Lieberman, Lubkin, and Bombieri. Credit moves through linked papers rather than one collective object.

The motives program has no single founding book. Credit must assemble letter, poster, short paper, Manin’s development, and later testimony without making the assembly look like a lost monograph.

These forms explain why one rule cannot settle the school’s authorship. Authorship operates differently for a treatise, seminar exposé, lecture-note book, conjecture, and program.

They also suggest a review test. For every noun phrase beginning “Grothendieck’s,” ask whether it names possession, origin, direction, or conventional terminology. Replace ambiguous possession with a verb and evidence.

The shorthand Grothendieck’s EGA becomes EGA, written by Grothendieck with Dieudonné’s documented collaboration.

“Grothendieck’s SGA 7 theorem” becomes the named exposé and author.

“Grothendieck’s proof of Weil” is removed; he did not give the 1974 proof.

“Grothendieck’s motives” becomes “the motivic program he originated,” followed by others’ constructions.

This editing discipline is ethical because grammar creates historical agents. It is also literary: precise verbs are stronger than possessives.

Credit, citation, and naming

Credit operates through several mechanisms. A theorem may carry an eponym. A paper may cite an origin. A title page may describe collaboration. A seminar volume may list exposés. A memoir may acknowledge influence. Tacit community knowledge may function for a time.

Eponyms are especially unreliable ledgers. The Grothendieck–Riemann–Roch theorem includes three historical names and many contributors to its formulations and proofs. The “Grothendieck topology” names an origin while its development involved Artin and others. The “Grothendieck group” can obscure context if treated as a personal brand.

Grothendieck himself attached evocative common nouns to concepts and sometimes attached others’ names to ideas. Serre used this earlier generosity to question his later grievance. The historical point is not inconsistency alone. Naming practices changed as ideas became standard and as Grothendieck’s relation to the community changed.

Citation answers a narrower question than credit. A citation directs readers to a text. An oral origin may have no citable publication. A later paper can cite the closest printed source and still omit the conversation that inspired it. Memoirs and correspondence help recover that layer, with lower certainty.

The safest response is dual citation: cite the proof and separately document the program or communication. This keeps readers able to verify mathematics without erasing origin.

Priority disputes often seek a first date. First mention, first definition, first proof, and first publication are different. The Grothendieck–Serre correspondence gives a first identified written mention of motives; the IHÉS seminar poster of April 1967 gives a public exposition; Manin’s paper gives the 1968 published construction. All three dates belong.

Naming can also overcredit through retrospective umbrella. If later mathematicians call several theories “motivic,” it does not follow that Grothendieck anticipated each construction. Historical relation requires a documented concept, problem, or line of influence.

Attribution is a claim like any other, not ornamental prose; the verbs of a mathematical sentence need the same checking as its equations.

Power to give, freedom to refuse

The deepest ethical symmetry of the departure concerns gifts. Motchane and IHÉS gave Grothendieck institutional conditions unusual in France, especially for a stateless mathematician. Grothendieck gave the institute prestige and a transformative program. He gave students problems and ideas. They gave proofs, writing, and years.

None of these gifts created ownership of the recipient.

IHÉS could not own Grothendieck’s conscience because it supported his work.

Grothendieck could not own Deligne’s institutional choice because he supported the appointment and training.

A student could not erase a communicated origin because the proof required original labor.

An originator could not demand a career as repayment for an idea freely given.

This symmetry does not make all obligations vanish. Gifts create gratitude, expectation, and relation. Ethical maturity distinguishes relation from enforceable command.

Deligne’s recollection records Grothendieck’s surprise and disappointment when he refused to resign. It does not establish the full expectations or private reasoning of either man. Deligne retained an independent institutional judgment.2424Jackson, “As If Summoned from the Void, II,” 1198.

At institutional scale, Grothendieck stated a condition for remaining and the board retained legal authority to decide on the grant. His later co-founding comparison is retrospective and is not used to infer his private reasoning in April 1970.

Departure was the act left when persuasion failed. It respected others’ formal freedom by withdrawing himself, even after attempts to recruit them. That fact is central to evaluating the ultimatum fairly.

In Récoltes et Semailles, Grothendieck later argued that ideas originating in the common work had been detached from adequate acknowledgment. Named former students and colleagues disputed the broader suppression claim. Both positions remain attributed retrospective accounts.2525Grothendieck, Récoltes et Semailles (Université des Sciences et Techniques du Languedoc and Centre National de la Recherche Scientifique, 1986); Jackson, “As If Summoned from the Void, II,” 1207–9.

No universal answer resolves every case. The minimum is truthful genealogy and freedom of future work.

What the title asks of the reader

“The Ethics of Departure” is not a claim that leaving was more ethical than staying. It names a field of obligations produced by both choices.

Grothendieck’s choice asks whether conscience may require relinquishing an institution one helped build. The record says yes for him.

Deligne’s and others’ choices ask whether intellectual loyalty requires following a mentor out. The record says they judged not.

The board’s choice asks whether nondirected military-origin support is compatible with pure science. The record gives its affirmative answer.

Michel and Ruelle’s proposal asks whether transition and earmarking can mediate principle. The record shows the proposal and its insufficiency.

Readers may judge these answers. The biography’s duty is to prevent judgment from resting on false sums, invented motives, or erased labor.

The title also asks readers to carry attribution forward. Every later statement about the Grothendieck school should remember that departure changed access and power. A theorem proved after 1970 may arise from earlier communication and later originality. Both dates matter.

Ethical biography does not end conflict through balanced adjectives. It makes claims traceable enough that disagreement can concern values rather than fabricated facts.

Five questions of credit

Every collaborative sentence in Part VII has to answer five questions.

Object. The concept, theorem, proof, paper, seminar, volume, or program must be specified before credit is assigned.

Act. Precise verbs include proposed, named, defined, proved, generalized, wrote, redacted, edited, and published. “Worked on” is usually too weak.

Source. A title page, exposé byline, contemporary paper, letter, archive record, or later recollection determines confidence.

Date. Seminar delivery, manuscript, and publication may differ. Priority claims need the earliest relevant act rather than the easiest date to find.

Dispute. Later accusations, independent discoveries, and changing terminology must appear where they affect the claim.

Applied to SGA 7, the checklist yields: Grothendieck proposed and directed a program; Deligne co-directed a documented phase and authored particular exposés; Katz authored lectures on Lefschetz pencils after a suggestion; later editors produced volumes in 1972–1973 from 1967–1969 work.

Applied to motives: Grothendieck named and framed the program; a 1964 letter and 1967 poster establish dates; Manin published a construction in 1968; standard conjectures supplied desired foundations; later categories have later authors.

Applied to resignation: the board made a funding decision; Grothendieck resigned; colleagues declined to follow; later memoirs interpreted. “Betrayed” requires a speaker and evidence.

Collective work after disagreement

Grothendieck’s later retrospective account emphasized mathematics as collective work. This unquoted claim does not imply harmony: collective mathematics can continue when participants cease sharing one institution or one moral judgment.2626Herreman, Découvrir et transmettre: La dimension collective des mathématiques dans *Récoltes et Semailles* d’Alexandre Grothendieck, 1 citing Récoltes et Semailles, p. 1234.

After 1970, the common adventure split into overlapping routes. Deligne and others pursued Weil, weights, Hodge theory, and related programs. Illusie developed cotangent complexes and deformation. Berthelot developed crystalline cohomology. Motives evolved through several schools. Grothendieck returned intermittently to new questions.

Calling all these routes his legacy can honor origin and flatten difference. Calling them independent can honor authors and erase the common starting terrain. “Divergent continuations” is often more accurate.

Departure made divergence visible because Grothendieck no longer coordinated weekly choices. It did not create every divergence. Students had already contributed original mathematics and joint direction.

The ethical possibility of a school depends on divergence. If students can only repeat, training has failed. If they erase what trained them, memory has failed. Mature inheritance combines freedom and genealogy.

The 1970 disagreement tested that combination outside mathematics. Deligne’s refusal enacted freedom; Grothendieck’s disappointment invoked relation. Neither act by itself establishes whether later genealogy was adequate.

This chapter leaves the credit disputes open at the level where they belong: individual texts, claims, and relationships. It rejects the false alternatives of a single-author legend versus an anonymous collective, gratitude versus independence, and service versus authorship.

The work was collective because individual acts remained distinguishable and connected. The departure was ethical because distinguishable people chose differently under connection.

The minimum record of respect

Respect in this history does not require agreement with Grothendieck’s later judgments. It requires naming what he originated and not using later conflict to diminish earlier work.

Respect for collaborators does not require diminishing his program. It requires naming proofs, redactions, and independent choices rather than describing people as extensions.

Respect for sources does not require accepting every testimony. It requires preserving date, speaker, and genre.

Respect for readers does not require hiding uncertainty for narrative flow. It requires telling them when a letter is missing and a motive inferred.

These requirements are modest compared with the moral claims in Récoltes et Semailles. They are enforceable in a biography.

The formal apparatus—fact cards, math cards, dispute cards, and byline audit—is not separate from literary justice. It makes persons recoverable after prose has compressed a decade.

The chapter’s final judgment is therefore procedural. The resignation was Grothendieck’s decision; staying was each colleague’s. The common mathematics remained open to continuation. Credit follows documented acts, not obedience.

That procedure cannot heal the relationships. It can prevent a new text from repeating their injuries through careless ownership.

Archives favor finished objects and official decisions. Collaboration often lives before both: a blackboard correction, an assigned question, a page returned with pencil, a lunch explanation. Later memory is needed to see those acts and too unstable to measure them alone.

The account of contributions therefore combines source types rather than ranking one universally. A title page governs formal authorship. A technical comparison can identify original mathematics. A recollection can explain process. A letter can date communication. Conflict claims require corroboration.

This mixed method mirrors the work itself. No single role made EGA or SGA; no single source can narrate their making. Ethical attribution begins by accepting that plurality.

Departure broke the routine in which participants could clarify roles face to face. The archive became more important just as the common understanding became less secure.

This is why authorship ethics belongs before, not after, the resignation. The break did not create the questions of origin, proof, and redaction. It removed the living arrangement that had allowed those questions to remain partly tacit.