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.
图 1 · 第 1 章
Hamburg within the German Empire of 1871. Milenioscuro. CC BY-SA 3.0. Wikimedia Commons, File:Hamburg in the German Reich (1871).svg.
图 2 · 第 3 章
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.
图 3 · 第 3 章
Map of Berlin-Mitte. Selfmade by Rumpeltux. CC BY-SA 2.0. Wikimedia Commons, File:Berlin Mitte map with listings.svg.
图 4 · 第 3 章
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.
图 5 · 第 4 章
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.
图 6 · 第 7 章
The regions and départements of France. Superbenjamin. CC BY-SA 4.0. Wikimedia Commons, File:France location map-Regions and departements-2016.svg.
图 7 · 第 7 章
The département of Ariège in France. Marmelad. CC BY-SA 2.5. Wikimedia Commons, File:Ariège-Position.svg.
图 8 · 第 7 章
The Camp du Vernet, Ariège: aerial photograph, 1945. IGN, Géoportail. CC BY-SA 4.0. Wikimedia Commons, File:Camp de vernet.jpg.
图 9 · 第 8 章
Carved rock at the site of the Rieucros camp, Mende (photographed 2008). Sanguinez. CC BY-SA 3.0. Wikimedia Commons, File:RieucrosRocherSculpte.jpg.
图 10 · 第 8 章
Street map of Mende. © OpenStreetMap contributors (map data ODbL). CC BY-SA 4.0. Wikimedia Commons, File:Mende OSM 02.png.
图 11 · 第 8 章
Mende, Lozère, seen from the Mont Mimat (photographed 2006). civodule. CC BY-SA 3.0. Wikimedia Commons, File:Mende-cathedrale-1.JPG.
图 12 · 第 8 章
The Gurs internment camp, around 1939. Unknown author. Public domain. Wikimedia Commons, File:Logor Gurs.jpg.
图 13 · 第 8 章
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.
图 14 · 第 9 章
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.
图 15 · 第 11 章
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.
图 16 · 第 11 章
Auschwitz I, the main camp (photographed 2010). Xiquinho Silva. CC BY 2.0. Wikimedia Commons, File:Auschwitz I (22 May 2010) b.jpg.
图 17 · 第 13 章
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.
图 18 · 第 16 章
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.
图 19 · 第 16 章
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.
图 20 · 第 16 章
Jean-Pierre Serre, Lille, October 2003. Mediterranean Institute for the Mathematical Sciences. CC BY 3.0. Wikimedia Commons, File:Jean-Pierre Serre 2003.jpg.
图 21 · 第 17 章
Roger Godement, 1984. Konrad Jacobs, Erlangen, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Roger Godement.jpg.
图 22 · 第 17 章
The Place Stanislas, Nancy (photographed 2013). Nicolas Cornet. CC BY-SA 4.0. Wikimedia Commons, File:Place Stanislas et ses grilles à Nancy.jpg.
图 23 · 第 17 章
The University of Nancy (photographed 2006). ~Pyb. CC BY-SA 2.5. Wikimedia Commons, File:Université de Nancy 003.jpg.
图 24 · 第 19 章
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.
图 25 · 第 20 章
The main campus of the University of Kansas, Lawrence (photographed 2007). JayhawkBrandon. Public domain. Wikimedia Commons, File:University of Kansas Main Campus.JPG.
图 26 · 第 21 章
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.
图 27 · 第 21 章
The diagram of the snake lemma: two exact rows and three vertical maps. Drawn for this edition.
图 28 · 第 21 章
A morphism of sheaves: the maps on sections commute with restriction. Drawn for this edition.
图 29 · 第 22 章
A commutative diagram. Drawn for this edition.
图 30 · 第 22 章
A functor preserves the composition of morphisms. Drawn for this edition.
图 31 · 第 22 章
A natural transformation viewed as a functor. Drawn for this edition.
图 32 · 第 22 章
Adjoint functors. Drawn for this edition.
图 33 · 第 22 章
A natural transformation between two functors. Drawn for this edition.
图 34 · 第 23 章
Armand Borel, Berkeley, 1975. George Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Armand Borel 1975 (headshot).jpg.
图 35 · 第 23 章
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.
图 36 · 第 23 章
Friedrich Hirzebruch at Berkeley, 1973. George M. Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Friedrich Hirzebruch 1973 (headshot).jpg.
图 37 · 第 23 章
The index theorem and the Grothendieck–Riemann–Roch theorem: the square commutes. Drawn for this edition.
图 38 · 第 24 章
The Togliatti surface. Claudio Rocchini. CC BY-SA 3.0. Wikimedia Commons, File:Togliatti surface.png.
图 39 · 第 24 章
The Tschirnhausen cubic. Theon. CC BY-SA 4.0. Wikimedia Commons, File:CubiqueTschirnhausen.svg.
图 40 · 第 24 章
Bézout’s theorem: two plane curves and their points of intersection. Kmhkmh. CC BY 4.0. Wikimedia Commons, File:Bezout theorem1.svg.
图 41 · 第 24 章
The Riemann surface of the logarithm. Tito Omburo. CC BY-SA 4.0. Wikimedia Commons, File:Log(z) Riemann surface.svg.
图 42 · 第 27 章
A fibre product (pullback) square. Drawn for this edition.
图 43 · 第 28 章
A pullback fibration. Drawn for this edition.
图 44 · 第 29 章
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.
图 45 · 第 31 章
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.
图 46 · 第 31 章
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.
图 47 · 第 32 章
The Möbius strip as a fibre bundle. JozumBjada. CC BY-SA 4.0. Wikimedia Commons, File:Fibre bundle - Moebius strip.png.
图 48 · 第 32 章
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.
图 49 · 第 32 章
The pullback of a fibre bundle. Drawn for this edition.
图 50 · 第 33 章
The constant sheaf on a space of two points. Drawn for this edition.
图 51 · 第 34 章
The elliptic curve y² = x³ − x. YassineMrabet. CC BY-SA 3.0. Wikimedia Commons, File:Elliptic curve y^2 = x^3 - x.svg.
图 52 · 第 34 章
Absolute and relative Frobenius morphisms. Drawn for this edition.
图 53 · 第 34 章
Homology cycles on a torus. Krishnavedala. CC0. Wikimedia Commons, File:Torus cycles Rr.svg.
图 54 · 第 35 章
Jacques Tits, Oslo, May 2008. Harald Hanche-Olsen. CC BY 3.0. Wikimedia Commons, File:Jacques Tits (2008) (cropped).jpg.
图 55 · 第 35 章
Barry Mazur, Berkeley, April 1992. George Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Barry Mazur, April 1992 (re-scanned, headshot).jpg.
图 56 · 第 35 章
Michel Demazure, Bures-sur-Yvette, 2007. Gert-Martin Greuel, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Michel Demazure.jpg.
图 57 · 第 35 章
Pierre Deligne, October 2005. copyright C. J. Mozzochi, Princeton N.J. Attribution. Wikimedia Commons, File:Pierre Deligne (2005) (cropped).jpg.
图 58 · 第 35 章
Pierre Cartier, Oberwolfach, 2009. Renate Schmid, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Pierre Cartier 2009.jpg.
图 59 · 第 36 章
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.
图 60 · 第 36 章
Moscow State University from the air (photographed 2015). I.s.kopytov. CC BY-SA 4.0. Wikimedia Commons, File:МГУ, вид с воздуха.jpg.
图 61 · 第 36 章
The obverse of the Fields Medal. Stefan Zachow for the International Mathematical Union. Public domain. Wikimedia Commons, File:FieldsMedalFront.jpg.
图 62 · 第 37 章
Stephen Smale, 2008. George Bergman. CC BY-SA 4.0. Wikimedia Commons, File:Stephen Smale, 2008 (cropped).jpg.
图 63 · 第 37 章
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.
图 64 · 第 37 章
Composite numbers arranged as rectangles; the primes cannot be. David Eppstein. CC0. Wikimedia Commons, File:Primes-vs-composites.svg.
图 65 · 第 37 章
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.
图 66 · 第 38 章
A catalogue of real elliptic curves. Tos. Public domain. Wikimedia Commons, File:EllipticCurveCatalog.svg.
图 67 · 第 41 章
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.
图 68 · 第 43 章
The main building of Bielefeld University (photographed 2012). Ub12vow. CC BY-SA 3.0. Wikimedia Commons, File:Bielefeld Uni Hauptgebäude 2012.jpg.
图 69 · 第 44 章
Demonstration against nuclear power, Bonn, 14 October 1979. Hans Weingartz. CC BY-SA 2.0 DE. Wikimedia Commons, File:ANTIAKW.jpg.
图 70 · 第 45 章
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.
图 71 · 第 49 章
The Place de la Comédie, Montpellier (photographed 2008). Wolfgang Staudt. CC BY 2.0. Wikimedia Commons, File:Montpellier Place de la Comédie.jpg.
图 72 · 第 50 章
A Möbius band cut once along its length. Ag2gaeh. CC BY-SA 4.0. Wikimedia Commons, File:Moebiusband-1s.svg.
图 73 · 第 51 章
The universal property of the fibre product of schemes. Drawn for this edition.
图 74 · 第 51 章
The entrance of the Université Montpellier 2 (photographed 2008). Vpe. CC BY-SA 3.0. Wikimedia Commons, File:Entreeum2.JPG.
图 75 · 第 52 章
The sheets of a covering space. Covering space diagram.jpg: Wordslaugh Splintercellguy. CC BY-SA 3.0. Wikimedia Commons, File:Covering space diagram.svg.
图 76 · 第 53 章
The hyperelliptic curve y² = x⁴ − x² + 1. Krishnavedala. CC BY-SA 3.0. Wikimedia Commons, File:Hyperelliptic curve.svg.
图 77 · 第 54 章
From varieties to schemes, algebraic spaces and stacks. Drawn for this edition.
图 78 · 第 55 章
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.
图 79 · 第 60 章
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.
图 80 · 第 62 章
Lasserre, Ariège (photographed 2023). Sergio09200. CC BY-SA 4.0. Wikimedia Commons, File:Lasserre (Ariège) - Vue générale.jpg.
图 81 · 第 63 章
Saint-Girons seen from the Cap du Garrié (photographed 2024). Géodigital. CC BY-SA 4.0. Wikimedia Commons, File:St-Girons vue Garrié.jpg.
图 82 · 第 66 章
Saint-Girons and the Sourroque mountain (photographed 2009). Olybrius. CC BY-SA 3.0. Wikimedia Commons, File:Saint-Girons and Sourroque.jpg.
图 83 · 第 66 章
Alexander Grothendieck’s grave, Lasserre (photographed 2025). Gustav Roch. CC0. Wikimedia Commons, File:Grothendiecks Grabstätte.jpg.
图 84 · 第 67 章
Leila Schneps, 2011. Natacha Colmez (uploaded by CoralieCC). CC BY-SA 3.0. Wikimedia Commons, File:Leila Schneps (2011).jpg.
图 85 · 第 69 章
Nicholas Katz, Oberwolfach, 2004. Renate Schmid, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Nicholas Katz.jpg.
图 86 · 第 69 章
Gérard Laumon, Oberwolfach, 2004. Renate Schmid, © MFO. CC BY-SA 2.0 DE. Wikimedia Commons, File:Gerard Laumon.jpg.
