Submission date: 23 March 2021

Abstract:

Peterzil and Steinhorn proved that if a group G definable in an o-minimal structure is not definably compact, then G contains a definable torsion-free subgroup of dimension one. We prove here a p-adic analogue of the Peterzil-Steinhorn theorem, in the special case of abelian groups. Let G be an abelian group definable in a p-adically closed field M. If G is not definably compact then there is a definable subgroup H of dimension one which is not definably compact. In a future paper we will generalize this to non-abelian G.

Mathematics Subject Classification: 03C60 (Primary) 03C98 (Secondary)

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Full text arXiv 2103.12427: pdf, ps.