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Scientific biography

Highlights of Grothendieck’s scientific path

Grothendieck’s scientific excellence was less due to solving the problems handed down by his predecessors than by his natural inclination that drove him to see questions, visibly crucial, that no one had seen, or to extract the ‘right concepts’ that were missing, as well as the ‘right statements’ that no one had thought of. Grothendieck’s lasting influence on mathematics is of such magnitude that it can be said that the great legacy of his ideas has crept in everywhere thanks to its foundational character and flexibility. Apart from his scientific output, he pondered deeply on the philosophical study of the nature of mathematical creativity, and his psychological apprehensions, as well as the scientists’ responsibility in the present-day world. We can only venture to predict an ever-increasing influence of his particular genius on future generations.

This section provides a timeline of A. Grothendieck’s scientific career, including his education, awards, honors received, and places where he worked, among other things. This profile is an essential resource for anyone interested in guiding insight into the rich context in which Grothendieck developed his enduring contribution to scientific thought.

  • 1945-1948: License studies (equivalent to Bachelor Studies) in mathematics at the University of Montpellier.
  • 1948-1949: Having obtained his degree, Grothendieck goes to Paris in view of obtaining a doctorate. He went as an “Auditeur libre” at the École Normale Supérieure in Paris. He took several courses, attended seminars, and met most of the famous mathematicians of the time, especially the members of the Bourbaki group.
  • 1950-1958: “Attaché de Recherche” at CNRS.
  • 1950-1969: This is the so-called ‘productive’ period of Grothendieck’s mathematical activity, meaning the period supported by proper publications and active engagements with the scientific community.
  • 1950-1953: Grothendieck goes to Nancy to make his doctoral studies under L. Schwartz (J. Dieudonné). He starts attending Bourbaki meetings as a “Cobaye”.
  • 1953-1954: Visiting research position at the Universidad de Sao Paulo (Brazil), and a short stay in Argentina.
  • 1955: Visiting research position at the University of Kansas (USA).
  • 1955-1960: Member of the Bourbaki group.
  • 1956-1970: Permanent stay in France, with the exception of numerous stays in the USA, notably at Harvard University, and other short stays that include Argentina (1954), Germany, Algeria (1966), Italy (1966 and 1969), the Democratic Republic of Vietnam (1967), India(1968), Romania (1969 and 1970), and Canada (1970).
  • 1958: Director of research CNRS.
  • 1959-1970: Professor at the Institut des Hautes Études Scientifiques (IHÉS). During these years he completely renews Algebraic geometry, writing EGA Éléments de Géométrie Algébrique (with Dieudonné) and SGA Séminaire de Géométrie Algébrique (with his students).
  • 1966: Fields Medal (International Congress of Mathematicians).
  • 1970-1973: In 1970, resigned from the IHÉS. He then held a guest professorship at the “Collège de France” for two years. Afterward, invited professorships at several Institutions including the University of Orsay, Kingston, Buffalo, and other short stays that include Romania and Germany. He gave lectures at the “International Congress of Mathematicians” also called the “Bourbaki ICM”. In particular, he delivered Hironaka’s laudation for the Fields medal. In the Summer of 1973, the news spread that Deligne had succeeded in finding proof of the final of the Weil conjectures.
  • 1973-1988: Professor at the University of Montpellier. He continues directing the research of graduate students and engaging in pedagogical endeavors. He retired definitively from major mathematical centers in the world.
  • 1977: Émile Picard Medal (Academy of Sciences).
  • 1983: Grothendieck kept working, while sporadically, on mathematical research, in 1983 he renovated profoundly his style of writing and started working in a long-term program entitled “Réflexions Mathématiques”.
  • 1984-1988: Discouraged by the teaching situation, Grothendieck applied for a temporary research position with the CNRS for the remaining years before his retirement. In his application, he presented a research program, the “Esquisse d’un programme”, which will become very influential.
  • 1988: Declined the Crafoord Prize (awarded alongside P. Deligne).
  • After 1988, the year of his retirement, Grothendieck continued writing mathematics; he kept evolving his methodology and style while also getting increasingly interested in philosophical questions.

Students

In the “Students” section, you will find a comprehensive list of Grothendieck’s numerous students, each making significant contributions to the advancement of mathematical knowledge in their own distinctive manner.

Explore their theses and gain insight into the subsequent publication process of their work. Join us in commemorating the collaborative spirit and enduring influence of Grothendieck’s mentorship, as we celebrate the remarkable achievements of his esteemed students in the field of mathematics.

First period

  • Michel Demazure (1964): Schémas en Groupes Réductives. Bull. SMF. 93 (1965), 369-413
  • Jean Giraud (1966): Cohomologie non Abélienne de degré 2. Published as Cohomologie non Abélienne. Grundlehren Math. Wissenshaften 179 Springer-Verlag (1971)
  • Jean-Louis Verdier (1967): Des catégories Dérivées des Catégories Abéliennes. SMF Astérisque 239 (1996).
  • Monique Hakim (1967): Schémas relatifs. Published as Topos Annelés et Schémas Relatifs. Ergebnisse Math. Gr. 64, Springer-Verlag (1972)
  •  Pierre Deligne (1968): Théorème de Lefschetz et critères de dégénérescence de suites spectrales. Publications Mathématiques de l’IHÉS. 35 (1968) pp. 107–126.
  • Michel Raynaud (1968): Faisceaux amples sur les schémas en groupes et les espaces homogènes. Lecture Notes in Mathematics (LNM, volume 119)
  • Jean-Pierre Jouanolou (1969): Catégories Dérivées en Cohomologie l-adique. Mathématiques [math]. Faculté des sciences de Paris, 1969. Français.
  • Luc Illusie (1971): Complexe Cotangent, Applications. Published as Complexe Cotangent et Déformations I, II. Springer Lecture Notes in Mathematics 264 (1972)
  • William Messing (1971): (Under A. Grothendieck and N. Katz). The Crystals Associated to Barsotti-Tate Groups: With Applications to Abelian Schemes. Springer Lecture Notes in Mathematics 264 (1972).
  • Pierre Deligne (1972): Théorie de Hodge I. Thèses d’Orsay, no. 13 (1972) , 56 p. 
  • Pierre Berthelot (1972): Cohomologie Cristalline des Schémas de Caractéristique p > 0. Springer Lecture Notes in Mathematics 407 (1974).
  • Michèle Raynaud (1972): Théorème de Lefschetz en Cohomologie Cohérente et en Cohomologie Étale. Mem. of SMF. 41 (1975).
  • Neantro Saavedra Rivano (1972): Catégories Tannakiennes. Springer Lecture Notes in Mathematics 265 (1972).
  • Hamet Seydi (1973): (Under A. Grothendieck and P. Samuel). Sur quelques chapitres choisis d’Algèbre Commutative et Conjecture de Serre en Géométrie Analytique.

Second period

  • Hoang Xuan Sinh (1975): Gr catégories. 1975 Orsay (doctorat d’état).
    • [scan]
    • [pdf] (Transcrption by Cristian David Gonzalez Avilés)
  • Amadou Diallo (1975) : Sur les ouverts affines des schémas affines. 1975 (thèse de spécialité).
  • Yves Ladegaillerie (1977): Découpe et isotopies en théorie des surfaces. 1977 (doctorat d’état).
  • Volker Diekert (1978): La théorie combinatoire de l’icosaèdre. Diplôme des Études Supérieures, 1977/78.
  • C. Voisin and J. Malgoire (1979): Factorisation de Stein topologiques, découpes. 1979 (thèses de 3 ème cycle).
  •  Olivier Leroy (1979): Groupoïde fondamental et théorème de van Kampen en théorie des topos. Cahiers mathématiques de l’université de Montpellier (1979). Under C. Contou-Carrère
  • Marcus Vinicius de Medeiros Wanderley (1980): Théorie inductive de l’orientation. 1980 (thèse de 3 ème cycle).
  • Pierre Damphousse (1981): Cartographie topologique. 1981 (thèse de 3ème cycle, Orsay) Under Norbert A Campo.
  • Carlos Contou-Carrère (1983): Géométrie des groupes semi-simples, résolutions équivariantes et lieu singulier de leurs variétés de Schubert. 1983
    (doctorat d’état).
  • El Aouni Allal (1984) : Étude d’une configuration remarquable d’un système de 9 pseudo-droites. 1984 (thèse de 3 ème cycle).
  • Mohammed Mellak (1987): Système de pseudo-droites. 1987 (thèse de 3ème cycle).
  • Philippe Delobel (1987): Combinatoire. 1987 (thèse de 3ème cycle).

Others

  • Gordon Edwards: Primitive and group-like elements in symmetric algebras. Canadian Journal of Mathematics, 1974 Lie Algebras of Infinitesimal Group Schemes, Queen’s University Ph.D. thesis, 1972.
  • Lucile Bégueri-Poitou: Dualité sur un corps local à corps résiduel algébriquement clos. Mémoires de la Société Mathématique de France, no. 4 (1980) , 124 p.
  • Max Karoubi: Algèbres de Clifford et K-théorie. Annales scientifiques de l’École Normale Supérieure, Serie 4, Volume 1 (1968) no. 2, pp. 161-270.

Eponymous

The “Eponymous” section stands as a tribute to the influence of A. Grothendieck on the realm of mathematics as a developing enterprise. These eponymous contributions span a wide spectrum of mathematical disciplines, reflecting the great breadth and depth of Grothendieck’s intellectual legacy. From algebraic geometry to number theory, his innovative ideas continue to shape the way mathematicians approach and unravel complex problems and new theories.

Exploring these eponymous also shows the enduring relevance of his work in contemporary mathematical research.

 

  • Ax–Grothendieck theorem
  • Birkhoff–Grothendieck theorem
  • Brieskorn–Grothendieck resolution
  • Dolbeault-Grothendieck lemma
  • Grothendieck’s axioms (Abelian categories)
  • Grothendieck category
  • Grothendieck’s comparison theorem (de Rham cohomology)
  • Grothendieck’s connectedness theorem
  • Grothendieck connection
  • Grothendieck construction
  • Grothendieck duality
  • Grothendieck existence theorem
  • Grothendieck fibration
  • Grothendieck group (K-theory)
  • Grothendieck’s homotopy hypothesis
  • Grothendieck local duality
  • Serre–Grothendieck–Verdier duality
  • Grothendieck-Köthe-Sebastiao e Silva duality (Holomorphic functions)
  • Grothendieck’s six operations
  • Grothendieck’s monodromy theorem
  • Grothendieck’s mysterious functor
  • Grothendieck–Ogg–Shafarevich formula
  • Grothendieck ring (of varieties)
  • Grothendieck polynomials
  • Grothendieck’s theorem (see Schlessinger’s theorem)
  • Grothendieck’s theorem (Fredholm kernel)
  • Grothendieck–Riemann–Roch theorem (Grothendieck–Hirzebruch–Riemann–Roch theorem)
  • Grothendieck’s vanishing theorem
  • Grothendieck space (Banach theory)
  • Grothendieck spectral sequence
  • Grothendieck bound
  • Grothendieck inequality or Grothendieck constant
  • Grothendieck norm
  • Grothendieck–Springer resolution
  • Grothendieck–Teichmüller group
  • Grothendieck-Witt ring
  • Grothendieck trace formula
  • Grothendieck trace theorem
  • Grothendieck pretopology
  • (Grothendieck) topoi
  • Grothendieck topology
  • Grothendieck universe
  • Tutte–Grothendieck invariant
  • Grothendieck’s anabelian conjectures
  • Grothendieck period conjecture
  • Grothendieck–Katz p-curvature conjecture
  • Grothendieck’s Galois theory
  • Grothendieck–Teichmüller theory
  • Tarski–Grothendieck set theory
  • Grothendieck’s Homotopy theory
  • Grothendieck’s relative point of view
  • Grothendieck prime
  • …

 

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