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Annales Scientifiques de l'École Normale Supérieure. Quatrième Série 39, 6 (2006) 871-920

Group-theoretic compactification of Bruhat-Tits buildings

Yves Guivarc'h 1, Bertrand Rémy 2

(2006)

Let GF 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 GF in the Chabauty topology, which enables 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 BruhatTits 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.

1:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
2:	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon

Subject

:

Mathematics/Group Theory

Keyword(s): semisimple algebraic group – local field – Bruhat-Tits building – geometric convergence – polyhedral compactification – amenability – distality

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From: Marie-Annick Guillemer <>

Submitted on: Thursday, 14 April 2005 11:32:32

Updated on: Monday, 15 March 2010 14:32:00