Chabauty limits of algebraic groups acting on trees

2016/10/26 by Thierry Stulemeijer, Stulemeijer, Thierry
Mathematics · #20E08 #20E42 #20F65 #20G25 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1610.08454

openalex publication_date 2016/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a locally finite leafless tree T , various algebraic groups over local fields might appear as closed subgroups of Aut (T). We show that the set of closed cocompact subgroups of Aut (T) that are isomorphic to a quasi-split simple algebraic group is a closed subset of the Chabauty space of Aut (T). This is done via a study of the integral Bruhat-Tits model of SL₂ and SU₃^L/K , that we carry on over arbitrary local fields, without any restriction on the (residue) characteristic. In particular, we show that in residue characteristic 2 , the Tits index of simple algebraic subgroups of Aut (T) is not always preserved under Chabauty limits.

Related

• A note on the structure theory of groups acting on the Bruhat Tits tree associated to PGL₂(F)
• Simple groups of automorphisms of trees determined by their actions on finite subtrees
• Groups Acting on Trees With Prescribed Local Action
• Chabauty limits of groups of involutions in SL(2,F) for local fields
• Groups acting on trees with Tits' independence property (P)