Sur la classification des schémas en groupes semi-simples

Philippe Gille (1, 2)

1 IMAR - "Simion Stoilow" Institute of Mathematics
2 AGL - Algèbre, géométrie, logique

We deal with the classification of semisimple group schemes via the Bruhat-Tits' presentation of non-abelian cohomology. The goal is to generalize Galois techniques to more general rings. It leads us to investigate the concept of reducibility for reductive group schemes with special attention to one parameter subgroups. It requires also the study of parabolic subgroups and their normalizers of a non-necessarily connected affine smooth group scheme G whose neutral component is reductive. The text discusses in an appendix also certain analogies for Weyl group schemes and twisted root data.

Mots clés: données radicielles; réductibilité; Schémas en groupes; sous-groupes paraboliques; isotropie

Domaines: Anneaux et algèbres [math.RA]; Géométrie algébrique [math.AG]

Philippe Gille. Sur la classification des schémas en groupes semi-simples. Panoramas et synthèses, 2016, 47, pp.39-110. ⟨hal-01063601v2⟩