Abstract
Let G F denote the rational points of a semisimple group G over a non-archimedean local field F, with Bruhat–Tits building X. This paper contains five main results. We prove a convergence theorem for sequences of parahoric subgroups of G F in the Chabauty topology, which enables us to compactify the vertices of X. We obtain a structure theorem showing that the Bruhat–Tits buildings of the Levi factors all lie in the boundary of the compactification. Then we obtain an identification theorem with the polyhedral compactification (previously defined in analogy with the case of symmetric spaces). We finally prove two parametrization theorems extending the Bruhat–Tits dictionary between maximal compact subgroups and vertices of X: one is about Zariski connected amenable subgroups and the other is about subgroups with distal adjoint action.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Annales Scientifiques de l’École Normale Supérieure
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
