Definable subgroups in SL_2 over a p-adically closed field

الأصل · EN

The aim of this paper is to describe all definable subgroups of SL2(K), for K a p-adically closed field. We begin by giving some "frame subgroups" which contain all nilpotent or solvable subgroups of SL2(K). A complete description is givien for K a p-adically closed field, some results are generalizable to K a field elementarily equivalent to a finite extension of Qp and an almost complete description is given for Q an p. We give also some indications about genericity and generosity in SL2(K).