Illustration Credits
86 figures. The figures of the book, with their authors, licences and sources, and the chapters that print them.
The figures by other authors keep their own licences. Each is reproduced unchanged except for conversion and scaling; the file pages give the full licence terms. The commutative diagrams were drawn for this edition.
Figure 1 · Chapter 1
Hamburg within the German Empire of 1871. Milenioscuro. CC BY-SA 3.0. Wikimedia Commons, File:Hamburg in the German Reich (1871).svg.
Figure 2 · Chapter 3
Stolperstein for Alexander Grothendieck, Brunnenstraße 165, Berlin-Mitte (photographed 2017). OTFW, Berlin. CC BY-SA 3.0. Wikimedia Commons, File:Stolperstein Brunnenstr 165 (Mitte) Alexander Grothendieck.jpg.
Figure 3 · Chapter 3
Map of Berlin-Mitte. Selfmade by Rumpeltux. CC BY-SA 2.0. Wikimedia Commons, File:Berlin Mitte map with listings.svg.
Figure 4 · Chapter 3
Stolperstein for Johanna (Hanka) Grothendieck, Brunnenstraße 165, Berlin-Mitte (photographed 2017). OTFW, Berlin. CC BY-SA 3.0. Wikimedia Commons, File:Stolperstein Brunnenstr 165 (Mitte) Johanna Hanka Grothendieck.jpg.
Figure 5 · Chapter 4
Stolperstein for Alexander Schapiro, Brunnenstraße 165, Berlin-Mitte (photographed 2017). OTFW, Berlin. CC BY-SA 3.0. Wikimedia Commons, File:Stolperstein Brunnenstr 165 (Mitte) Alexander Schapiro.jpg.
Figure 6 · Chapter 7
The regions and départements of France. Superbenjamin. CC BY-SA 4.0. Wikimedia Commons, File:France location map-Regions and departements-2016.svg.
Figure 7 · Chapter 7
The département of Ariège in France. Marmelad. CC BY-SA 2.5. Wikimedia Commons, File:Ariège-Position.svg.
Figure 8 · Chapter 7
The Camp du Vernet, Ariège: aerial photograph, 1945. IGN, Géoportail. CC BY-SA 4.0. Wikimedia Commons, File:Camp de vernet.jpg.
Figure 9 · Chapter 8
Carved rock at the site of the Rieucros camp, Mende (photographed 2008). Sanguinez. CC BY-SA 3.0. Wikimedia Commons, File:RieucrosRocherSculpte.jpg.
Figure 10 · Chapter 8
Street map of Mende. © OpenStreetMap contributors (map data ODbL). CC BY-SA 4.0. Wikimedia Commons, File:Mende OSM 02.png.
Figure 11 · Chapter 8
Mende, Lozère, seen from the Mont Mimat (photographed 2006). civodule. CC BY-SA 3.0. Wikimedia Commons, File:Mende-cathedrale-1.JPG.
Figure 12 · Chapter 8
The Gurs internment camp, around 1939. Unknown author. Public domain. Wikimedia Commons, File:Logor Gurs.jpg.
Figure 13 · Chapter 8
Gurs in the arrondissement of Oloron-Sainte-Marie, Pyrénées-Atlantiques. FCK-Iceman. CC BY-SA 4.0. Wikimedia Commons, File:Gurs (Pyrénées-Atlantiques) dans son Arrondissement.png.
Figure 14 · Chapter 9
The town hall of Le Chambon-sur-Lignon (photographed 2010). Havang(nl). CC0. Wikimedia Commons, File:Le Chambon-sur-Lignon (Haute-Loire, Fr) mairie.JPG.
Figure 15 · Chapter 11
The Drancy internment camp, August 1941. Bundesarchiv, Bild 183-B10919 / Wisch. CC BY-SA 3.0 DE. Wikimedia Commons, File:Bundesarchiv Bild 183-B10919, Frankreich, Internierungslager Drancy.jpg.
Figure 16 · Chapter 11
Auschwitz I, the main camp (photographed 2010). Xiquinho Silva. CC BY 2.0. Wikimedia Commons, File:Auschwitz I (22 May 2010) b.jpg.
Figure 17 · Chapter 13
The medical school of Montpellier, on an early postcard. Wellcome Collection. CC BY 4.0. Wikimedia Commons, File:The medical school of Montpellier, France Wellcome V0049871.jpg.
Figure 18 · Chapter 16
left. Henri Cartan, 1968. Konrad Jacobs, Erlangen. CC BY-SA 2.0 DE. Wikimedia Commons, File:Henri Cartan.jpg.
centre. Jean Leray at Oberwolfach, 1961. Konrad Jacobs. CC BY-SA 2.0 DE. Wikimedia Commons, File:Jean Leray.jpeg.
right. Jean Dieudonné, 1970. Konrad Jacobs, Erlangen. CC BY-SA 2.0 DE. Wikimedia Commons, File:Jean Dieudonné.jpg.
Figure 19 · Chapter 16
The entrance of the École normale supérieure, Paris (photographed 2013). Guilhem Vellut. CC BY 2.0. Wikimedia Commons, File:École normale supérieure de Paris, 26 January 2013.jpg.
Figure 20 · Chapter 16
Jean-Pierre Serre, Lille, October 2003. Mediterranean Institute for the Mathematical Sciences. CC BY 3.0. Wikimedia Commons, File:Jean-Pierre Serre 2003.jpg.
Figure 21 · Chapter 17
Roger Godement, 1984. Konrad Jacobs, Erlangen, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Roger Godement.jpg.
Figure 22 · Chapter 17
The Place Stanislas, Nancy (photographed 2013). Nicolas Cornet. CC BY-SA 4.0. Wikimedia Commons, File:Place Stanislas et ses grilles à Nancy.jpg.
Figure 23 · Chapter 17
The University of Nancy (photographed 2006). ~Pyb. CC BY-SA 2.5. Wikimedia Commons, File:Université de Nancy 003.jpg.
Figure 24 · Chapter 19
The campus of the University of São Paulo (photographed 2016). Mike Peel. CC BY-SA 4.0. Wikimedia Commons, File:University of Sao Paulo campus 2016 008.jpg.
Figure 25 · Chapter 20
The main campus of the University of Kansas, Lawrence (photographed 2007). JayhawkBrandon. Public domain. Wikimedia Commons, File:University of Kansas Main Campus.JPG.
Figure 26 · Chapter 21
Saunders Mac Lane (left) and Samuel Eilenberg at the Isle of Thorns meeting on category theory, 1992. Charles Wells (SixWingedSeraph). CC BY-SA 4.0. Wikimedia Commons, File:Eilenberg and Mac Lane at the Isle of Thorns.jpg.
Figure 27 · Chapter 21
The diagram of the snake lemma: two exact rows and three vertical maps. Drawn for this edition.
Figure 28 · Chapter 21
A morphism of sheaves: the maps on sections commute with restriction. Drawn for this edition.
Figure 29 · Chapter 22
A commutative diagram. Drawn for this edition.
Figure 30 · Chapter 22
A functor preserves the composition of morphisms. Drawn for this edition.
Figure 31 · Chapter 22
A natural transformation viewed as a functor. Drawn for this edition.
Figure 32 · Chapter 22
Adjoint functors. Drawn for this edition.
Figure 33 · Chapter 22
A natural transformation between two functors. Drawn for this edition.
Figure 34 · Chapter 23
Armand Borel, Berkeley, 1975. George Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Armand Borel 1975 (headshot).jpg.
Figure 35 · Chapter 23
The integers as a Grothendieck group: the sum (−2) + 1 = −1. Melchoir. CC BY-SA 3.0. Wikimedia Commons, File:Addition of integers using Grothendieck construction.svg.
Figure 36 · Chapter 23
Friedrich Hirzebruch at Berkeley, 1973. George M. Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Friedrich Hirzebruch 1973 (headshot).jpg.
Figure 37 · Chapter 23
The index theorem and the Grothendieck–Riemann–Roch theorem: the square commutes. Drawn for this edition.
Figure 38 · Chapter 24
The Togliatti surface. Claudio Rocchini. CC BY-SA 3.0. Wikimedia Commons, File:Togliatti surface.png.
Figure 39 · Chapter 24
The Tschirnhausen cubic. Theon. CC BY-SA 4.0. Wikimedia Commons, File:CubiqueTschirnhausen.svg.
Figure 40 · Chapter 24
Bézout’s theorem: two plane curves and their points of intersection. Kmhkmh. CC BY 4.0. Wikimedia Commons, File:Bezout theorem1.svg.
Figure 41 · Chapter 24
The Riemann surface of the logarithm. Tito Omburo. CC BY-SA 4.0. Wikimedia Commons, File:Log(z) Riemann surface.svg.
Figure 42 · Chapter 27
A fibre product (pullback) square. Drawn for this edition.
Figure 43 · Chapter 28
A pullback fibration. Drawn for this edition.
Figure 44 · Chapter 29
The town hall of Bures-sur-Yvette (photographed 2009). En-bateau. CC BY-SA 3.0. Wikimedia Commons, File:Bures sur Yvette Hôtel de Ville.jpg.
Figure 45 · Chapter 31
Jean-Louis Verdier (right) with Emma Previato, Oberwolfach, 1984. Konrad Jacobs, Erlangen, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Verdier Previato.jpg.
Figure 46 · Chapter 31
Luc Illusie lecturing at the IHÉS, 2014 (still from a video). Vincent Mia Edie Verheyen. CC BY-SA 4.0. Wikimedia Commons, File:Luc Illusie, Around the Thom-Sebastiani theorem, Journées de géométrie arithmétique de l’IHÉS, Conference center Marilyn and James Simons (Bures sur Yvette, France), 25 September 2014.png.
Figure 47 · Chapter 32
The Möbius strip as a fibre bundle. JozumBjada. CC BY-SA 4.0. Wikimedia Commons, File:Fibre bundle - Moebius strip.png.
Figure 48 · Chapter 32
The connection form of a principal bundle as a projection. Tazerenix. CC BY-SA 4.0. Wikimedia Commons, File:Principal bundle connection form projection.png.
Figure 49 · Chapter 32
The pullback of a fibre bundle. Drawn for this edition.
Figure 50 · Chapter 33
The constant sheaf on a space of two points. Drawn for this edition.
Figure 51 · Chapter 34
The elliptic curve y² = x³ − x. YassineMrabet. CC BY-SA 3.0. Wikimedia Commons, File:Elliptic curve y^2 = x^3 - x.svg.
Figure 52 · Chapter 34
Absolute and relative Frobenius morphisms. Drawn for this edition.
Figure 53 · Chapter 34
Homology cycles on a torus. Krishnavedala. CC0. Wikimedia Commons, File:Torus cycles Rr.svg.
Figure 54 · Chapter 35
Jacques Tits, Oslo, May 2008. Harald Hanche-Olsen. CC BY 3.0. Wikimedia Commons, File:Jacques Tits (2008) (cropped).jpg.
Figure 55 · Chapter 35
Barry Mazur, Berkeley, April 1992. George Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Barry Mazur, April 1992 (re-scanned, headshot).jpg.
Figure 56 · Chapter 35
Michel Demazure, Bures-sur-Yvette, 2007. Gert-Martin Greuel, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Michel Demazure.jpg.
Figure 57 · Chapter 35
Pierre Deligne, October 2005. copyright C. J. Mozzochi, Princeton N.J. Attribution. Wikimedia Commons, File:Pierre Deligne (2005) (cropped).jpg.
Figure 58 · Chapter 35
Pierre Cartier, Oberwolfach, 2009. Renate Schmid, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Pierre Cartier 2009.jpg.
Figure 59 · Chapter 36
Soviet stamp for the International Congress of Mathematicians, Moscow, 1966. USSR Post. Public domain. Wikimedia Commons, File:The Soviet Union 1966 CPA 3310 stamp (The International Congress of Mathematicians (ICM) (16-26.08, Moscow). Emblem - Integral Symbol and Globe. Sum and Union Symbols).jpg.
Figure 60 · Chapter 36
Moscow State University from the air (photographed 2015). I.s.kopytov. CC BY-SA 4.0. Wikimedia Commons, File:МГУ, вид с воздуха.jpg.
Figure 61 · Chapter 36
The obverse of the Fields Medal. Stefan Zachow for the International Mathematical Union. Public domain. Wikimedia Commons, File:FieldsMedalFront.jpg.
Figure 62 · Chapter 37
Stephen Smale, 2008. George Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Stephen Smale, 2008 (cropped).jpg.
Figure 63 · Chapter 37
Michael Atiyah at a symposium in honour of Shiing-Shen Chern, Berkeley, April 1996. George M. Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Michael Atiyah at a 1996 Chern symposium (portion B, 1300 dpi).jpg.
Figure 64 · Chapter 37
Composite numbers arranged as rectangles; the primes cannot be. David Eppstein. CC0. Wikimedia Commons, File:Primes-vs-composites.svg.
Figure 65 · Chapter 37
left. Lars Hörmander, Tokyo, 1969. Konrad Jacobs. CC BY-SA 2.0 DE. Wikimedia Commons, File:Lars Hörmander.jpg.
right. René Thom, Nice, 1970. Konrad Jacobs, Erlangen. CC BY-SA 2.0 DE. Wikimedia Commons, File:René Thom.jpeg.
Figure 66 · Chapter 38
A catalogue of real elliptic curves. Tos. Public domain. Wikimedia Commons, File:EllipticCurveCatalog.svg.
Figure 67 · Chapter 41
Demonstrators in the Place du Capitole, Toulouse, June 1968. André Cros. CC BY-SA 4.0. Wikimedia Commons, File:11-12.06.68 Mai 68. Nuit d’émeutes. Manif. Barricades.Dégâts (1968) - 53Fi1037.jpg.
Figure 68 · Chapter 43
The main building of Bielefeld University (photographed 2012). Ub12vow. CC BY-SA 3.0. Wikimedia Commons, File:Bielefeld Uni Hauptgebäude 2012.jpg.
Figure 69 · Chapter 44
Demonstration against nuclear power, Bonn, 14 October 1979. Hans Weingartz. CC BY-SA 2.0 DE. Wikimedia Commons, File:ANTIAKW.jpg.
Figure 70 · Chapter 45
South Vietnamese troops airlifted by U.S. Army helicopters near Khâm Đức, July 1970. U.S. Air Force. Public domain. Wikimedia Commons, File:U.S. Army UH-1H Hueys insert ARVN troops at Khâm Đức, Vietnam, 12 July 1970 (79431435).jpg.
Figure 71 · Chapter 49
The Place de la Comédie, Montpellier (photographed 2008). Wolfgang Staudt. CC BY 2.0. Wikimedia Commons, File:Montpellier Place de la Comédie.jpg.
Figure 72 · Chapter 50
A Möbius band cut once along its length. Ag2gaeh. CC BY-SA 4.0. Wikimedia Commons, File:Moebiusband-1s.svg.
Figure 73 · Chapter 51
The universal property of the fibre product of schemes. Drawn for this edition.
Figure 74 · Chapter 51
The entrance of the Université Montpellier 2 (photographed 2008). Vpe. CC BY-SA 3.0. Wikimedia Commons, File:Entreeum2.JPG.
Figure 75 · Chapter 52
The sheets of a covering space. Covering space diagram.jpg: Wordslaugh Splintercellguy. CC BY-SA 3.0. Wikimedia Commons, File:Covering space diagram.svg.
Figure 76 · Chapter 53
The hyperelliptic curve y² = x⁴ − x² + 1. Krishnavedala. CC BY-SA 3.0. Wikimedia Commons, File:Hyperelliptic curve.svg.
Figure 77 · Chapter 54
From varieties to schemes, algebraic spaces and stacks. Drawn for this edition.
Figure 78 · Chapter 55
The headquarters of the CNRS, rue Michel-Ange, Paris (photographed 2018). Celette. CC BY-SA 4.0. Wikimedia Commons, File:Siège du CNRS rue Michel-Ange Paris 2.jpg.
Figure 79 · Chapter 60
The hamlet of Ussau, Montégut-en-Couserans, Ariège (photographed 2011). Olybrius. CC BY-SA 3.0. Wikimedia Commons, File:Montégut-en-Couserans - Ussau - 20110702 (1).JPG.
Figure 80 · Chapter 62
Lasserre, Ariège (photographed 2023). Sergio09200. CC BY-SA 4.0. Wikimedia Commons, File:Lasserre (Ariège) - Vue générale.jpg.
Figure 81 · Chapter 63
Saint-Girons seen from the Cap du Garrié (photographed 2024). Géodigital. CC BY-SA 4.0. Wikimedia Commons, File:St-Girons vue Garrié.jpg.
Figure 82 · Chapter 66
Saint-Girons and the Sourroque mountain (photographed 2009). Olybrius. CC BY-SA 3.0. Wikimedia Commons, File:Saint-Girons and Sourroque.jpg.
Figure 83 · Chapter 66
Alexander Grothendieck’s grave, Lasserre (photographed 2025). Gustav Roch. CC0. Wikimedia Commons, File:Grothendiecks Grabstätte.jpg.
Figure 84 · Chapter 67
Leila Schneps, 2011. Natacha Colmez (uploaded by CoralieCC). CC BY-SA 3.0. Wikimedia Commons, File:Leila Schneps (2011).jpg.
Figure 85 · Chapter 69
Nicholas Katz, Oberwolfach, 2004. Renate Schmid, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Nicholas Katz.jpg.
Figure 86 · Chapter 69
Gérard Laumon, Oberwolfach, 2004. Renate Schmid, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Gerard Laumon.jpg.
