Quotients compacts des groupes ultrametriques de rang un

Details Quotients compacts des groupes ultrametriques de rang un Quotients compacts des groupes ultrametriques de rang un

2009-04-29

arxiv.org/abs/0904.4657v1

Mathematics

Group Theory

35 pages, 5 figures

Scientific paper

Let G be the set of k-points of a connected semisimple algebraic group of k-rank one over a nonarchimedean local field k. We describe all finitely generated torsion-free discrete subgroups of G\times G acting properly discontinuously and cocompactly on G by left and right multiplication. We prove that after a small deformation in G\times G such a discrete subgroup keeps acting freely, properly discontinuously, and cocompactly on G. ----- Soit G l'ensemble des k-points d'un groupe algebrique semi-simple connexe de k-rang un sur un corps local ultrametrique k. Nous decrivons tous les sous-groupes discrets de type fini sans torsion de G\times G qui agissent proprement et cocompactement sur G par multiplication a gauche et a droite. Nous montrons qu'apres une petite deformation dans G\times G un tel sous-groupe discret agit encore librement, proprement et cocompactement sur G.

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