Submission date: 27 January 2015.

Abstract:

The aim of this paper is to describe all definable subgroups of SL_2(K), for K a p-adically closed field. We begin by giving some “frame subgroups” which contain all nilpotent or solvable subgroups of SL_2(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 Q_p and an almost complete description is given for Q_p^{an} . We give also some indications about genericity and generosity in SL_2(K).

Mathematics Subject Classification: 03C60, 20G25

Keywords and phrases: Cartan subgroups, p-adics, semialgebraic and subanalytic subgroups, generosity.

Full text arXiv 1501.06834: pdf, ps.