On profinite subgroups of an algebraic group over a local field

Benoit Loisel (1, 2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

The purpose of this paper is to link anisotropy properties of an algebraic group together with compactness issues in the topological group of its rational points. We nd equivalent conditions on a smooth ane algebraic group scheme over a non-Archimedean local eld for the associated rational points to admit maximal compact subgroups. We use the structure theory of pseudo-reductive groups provided, whatever the characteristic, by Conrad, Gabber and Prasad. We also investigate thoroughly maximal prop subgroups in the semisimple case, using Bruhat-Tits theory.

Mots clés: Bruhat-Tits buildings; locally compact groups; quasi-reductive groups; integral models

Domaines: Théorie des groupes [math.GR]; Géométrie algébrique [math.AG]

Benoit Loisel. On profinite subgroups of an algebraic group over a local field. Transformation Groups, 2019, 24 (4), pp.1173-1211. ⟨hal-01346648v4⟩