Pierre Gabriel also often as Peter Gabriel (1933-2015) was a French and Swiss mathematician, professor at Zürich, was a president of Swiss Mathematical Society in 1980/1981.
The English wikipedia gives almost nothing, but there is some bio material at German wikipedia and similarly at the French wikipedia page).
Students of Gabriel include Bernhard Keller.
A version of Gabriel’s 1960 PhD thesis has been published as Des catégories abéliennes in 1962. His thesis was a major breakthrough in the theory of localization, and the study of abelian categories, including categories of quasicoherent sheaves on schemes. In retrospective, it can be said that it was in its ideas and methods one of the starting points of modern noncommutative algebraic geometry as well.
Gabriel assisted Grothendieck in reformulating the pseudofunctor version of descent theory in invariant (property characterized way) i.e. as fibered categories which he wrote up under the guidance of Grothendieck in SGA I.6. Gabriel contributed to some other parts of SGA, namely in study of group schemes and formal schemes, e.g. in SGA III.2 (Exp. 7a, P. Gabriel, Étude infinitésimale des schémas en groupe et groupes formels; Exp. 7b, P. Gabriel, Groupes formels). Soon after with Demazure writes a first tome of an unfinished but monumental work on algebraic groups which, more than EGA, emphasised functor of points view.
On abelian categories and Gabriel localization:
Pierre Gabriel, Des Categories Abeliennes, Bulletin de la Société Mathématique de France 90 (1962) 323-448 [numdam:BSMF_1962__90__323_0]
Pierre Gabriel, La localisation dans les anneaux non commutatifs, Séminaire Dubreil (1959-1960) exposé 2, 1-35 [numdam:SD_1959-1960__13_1_A2_0, pdf]
On algebraic schemes and algebraic groups via functorial geometry:
Michel Demazure, Pierre Gabriel, Groupes algebriques, tome 1, avec un appendice Corps de classes local par Hazewinkel M, Mason and Cie, Paris (1970)
(later volumes never appeared)
English translation:
Early monograph on the calculus of fractions for localizations of categories:
Introducing the notion of locally presentable categories:
In later part of his mathematical career, Gabriel worked on representation theory of finite-dimensional associative algebras and quivers, where he found some of the basic theorems, see Gabriel's theorem.
Gabriel-Rosenberg reconstruction theorem,
Gabriel-Zisman localization
Last revised on May 30, 2024 at 16:36:35. See the history of this page for a list of all contributions to it.