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arXiv · 1501.06834

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

Benjamin Druart
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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).

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Benjamin Druart. 2015-01-27. Definable subgroups in $SL\_2$ over a p-adically closed field. https://arxiv.org/abs/1501.06834

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