Life and work of Alexander Grothendieck (Q679554)

This short biography of Alexander Grothendieck and survey of his work in algebraic geometry features a personal tone by recollections of the second author and a letter sent to him by Grothendieck, dated 3 February 2010 and reproduced in facsimile. The survey gives a chronological account, focussing on homological algebra [\textit{A. Grothendieck}, Tohoku Math. J. (2) 9, 119--221 (1957; Zbl 0118.26104)], schemes, the algebraic fundamental group, descent theory [\textit{A. Grothendieck}, in: Séminaire de géométrie algébrique du Bois Marie 1960/61: revêtements étales et groupe fondamental (SGA~1). Berlin-Heidelberg-New York: Springer-Verlag (1971; Zbl 0234.14002); Fondements de la géométrie algébrique: extraits du séminaire Bourbaki 1957--1962. Paris: Secrétariat mathématique (1962; Zbl 0239.14002)], Grothendieck topologies [\textit{M. Demazure}, in: Séminaire de géométrie algébrique 1962/64: schémas en groupes (SGA~3), I: Propriétés générales des schémas en groupes. Berlin-Heidelberg-New York: Springer-Verlag (1970; Zbl 0207.51401)], étale cohomology [\textit{L. Illusie}, in: Alexandre Grothendieck: a mathematical portrait. Somerville, MA: International Press. 175--192 (2014; Zbl 1303.14007)], and the monodromy theorem [\textit{J.-P. Serre} and \textit{J. Tate}, Ann. Math. (2) 88, 492--517 (1968; Zbl 0172.46101)]. In particular, schemes with nilpotents in the structure sheaf are presented through the example of the Picard functor.