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Article Dans Une Revue Annales Scientifiques de l'École Normale Supérieure Année : 2006

Group-theoretic compactification of Bruhat-Tits buildings

Yves Guivarc'H
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Bertrand Rémy
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Résumé

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.
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Dates et versions

hal-00004700 , version 1 (14-04-2005)

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Yves Guivarc'H, Bertrand Rémy. Group-theoretic compactification of Bruhat-Tits buildings. Annales Scientifiques de l'École Normale Supérieure, 2006, 39 (6), pp.871-920. ⟨hal-00004700⟩
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