Alexander Grothendieck

Alexander Grothendieck

Born: March 28th, 1928 in Berlin, Germany

A concise quote from an article by J J O'Connor and E F Robertson:

Alexander Grothendieck's father was Russian and he (Alex's father) was murdered by the Nazis.” ... (His mother, Hanka Grothendieck, was German); ...“Grothendieck moved to France in 1941 and later entered Montpellier University. After graduating from Montpellier he spent the year 1948-49 at the École Normale Supérieure in Paris.”

Alex's `Golden Age'

Alexander Grothendieck's work during the `Golden Age' period established unifying themes in:

Algebraic Geometry, Number Theory, Topology, category theory and Functional/Complex Analysis. Alex introduced his own `theory of schemes' in the 1960's which allowed certain of A. Weil's number theory conjectures to be solved. He worked on the theory of topoi/toposes that are relevant not only to mathematical logic and category theory, but also to computer software/ and institutional ontology classification and bioinformatics. He provided an algebraic proof of the Riemann-Roch theorem, algebraic definition of the fundamental group of a curve, the definition of the fundamental functor for a categorical Galois theory, the re-definition of abelian categories,(as for example in the case of $ \mathcal Ab5$ categories that carry his name-the Grothendieck and local Grothendieck categories), he outlined the `Dessins d' Enfants' combinatorial topology theory and much, much more. His Séminaires de Géometrie algèbriques alone are several thousands of pages in (typewritten) printed length, or close to 500 Mb in electronic format. Later in the '80's in his `Esquisse d'un Programme' he outlined the `anabelian' homology theory, what is called today in different fields by different names: non-Abelian Homology Theory (that has not yet been achieved as he planned to do), non-Abelian algebraic topology, noncommutative geometry, Non-Abelian quantum field theories, or ultimately, non-Abelian categorical ontology, fields that are still in need of future developments.

1970-72 Visiting Professor at Collège de France,

1972-73 Visiting Professor at Orsay.

1973 Professor at the University of Montpellier; 1984-88 On leave- to direct research at the Centre National de la Recherche Scientifique.

Honors and Awards

Author's Direct, First Hand Impressions of Alexander Grothendieck:

One was struck immediately upon meeting him by his generosity and the energy with which Alex shared his ideas with colleagues and students, as well as the excitement that he incited through his brilliantly clear lecturing style, thus inspiring others to share in his excitement for all of Mathematics, not just some highly specialized subject, as if they were `to set out to explore a completely new land, or white territory'.

A Brief Summary of some of Alexander Grothendieck's best-known Contributions to Mathematics:

Note: Alexander Grothendieck's mathematical `genealogy' is claimed to go back through many successive doctoral advisor generations from Laurent Schwartz to Borel, Darboux,..., Simeon Poisson, Joseph Lagrange, Leonhard Euler, Bernoulli, Gottfried Leibniz (in 1666, with a 53,763-long sequence of `descendants'), Weigel and Christiaan Huygens, and the record finally stops at Ludolph van Ceulen at the Universiteit Leiden in 1607 AD!

A most valuable resource in Algebraic Geometry, “Ho- and Coho- mology”:
Grothendieck-Serre Correspondence-Bilingual Edn.

Bibliography

1
Winfried Scharlau: ``Who Is Alexander Grothendieck ?''

2
Alexander Grothendieck. 1971, Revêtements Étales et Groupe Fondamental (SGA1), chapter VI: Catégories fibrées et descente, Lecture Notes in Math. 224, Springer-Verlag: Berlin.

3
Alexander Grothendieck. 1957, Sur quelque point d-algèbre homologique. , Tohoku Math. J., 9: 119-121.

4
Alexander Grothendieck and J. Dieudoné.: 1960, Eléments de geometrie algèbrique., Publ. Inst. des Hautes Etudes de Science, 4.

5
Alexander Grothendieck et al.,1971. Séminaire de Géométrie Algèbrique du Bois-Marie, Vol. 1-7, Berlin: Springer-Verlag.

6
Alexander Grothendieck. 1962. Séminaires en Géométrie Algébrique du Bois-Marie, Vol. 2 - Cohomologie Locale des Faisceaux Cohèrents et Théorèmes de Lefschetz Locaux et Globaux. , pp.287. (with an additional contributed exposé by Mme. Michele Raynaud). Typewritten manuscript available in French; see also a brief summary in English References Cited:
  1. J. P. Serre. 1964. Cohomologie Galoisienne, Springer-Verlag: Berlin.
  2. J. L. Verdier. 1965. Algèbre homologiques et Catégories derivées. North Holland Publ. Cie.

7
Alexander Grothendieck. 1957, Sur Quelques Points d'algèbre homologique, Tohoku Mathematics Journal, 9, 119-221.

8
Alexander Grothendieck et al. Séminaires en Géometrie Algèbrique- 4, Tome 1, Exposé 1 (or the Appendix to Exposée 1, by `N. Bourbaki' for more detail and a large number of results. AG4 is freely available in French; also available here is an extensive Abstract in English.

9
Alexander Grothendieck, 1984. ``Esquisse d'un Programme'', (1984 manuscript), finally published in ``Geometric Galois Actions'', L. Schneps, P. Lochak, eds., London Math. Soc. Lecture Notes 242, Cambridge University Press, 1997, pp.5-48; English transl., ibid., pp. 243-283. MR 99c:14034 .

10
Alexander Grothendieck, ``La longue marche in à travers la théorie de Galois'' = ``The Long March Towards/Across the Theory of Galois'', 1981 manuscript, University of Montpellier preprint series 1996, edited by J. Malgoire.

11
Leila Schneps. 1994. The Grothendieck Theory of Dessins d'Enfants. (London Mathematical Society Lecture Note Series), Cambridge University Press, 376 pp.

12
David Harbater and Leila Schneps. 2000. Fundamental groups of moduli and the Grothendieck-Teichmüller group, Trans. Amer. Math. Soc. 352 (2000), 3117-3148. MSC: Primary 11R32, 14E20, 14H10; Secondary 20F29, 20F34, 32G15.



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