2016/07/31 by Benoit Loisel, B. LOISEL
Mathematics · #Advanced Algebra and Geometry #Affine transformation #Algebraic Geometry and Number Theory #Algebraic group #Algebraic number #Compact group #Compact space #Field (mathematics) #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Local field #Profinite group #Topological group #math.AG #math.GR
paper · pdf · doi:10.1007/s00031-019-09545-4
openalex created_date 2016/08/23 · arxiv created 2019/10/09 · openalex publication_date 2019/11/16 · arxiv updated 2020/01/07 · openalex updated_date 2026/08/05
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.