Definable subgroups in $SL\_2$ over a p-adically closed field

Abstract

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).

References in corpus (1)

• Pseudo real closed field, pseudo p-adically closed fields and NTP2

Cited by in corpus (1)

• Some model theory and topological dynamics of p-adic algebraic groups