On simple groups definable in some valued fields
Logic
2026-01-14 v1 Commutative Algebra
Algebraic Geometry
Group Theory
Abstract
We prove that non-abelian definable, definably simple groups in 1-h-minimal henselian valued fields are essentially already linear algebraic groups. Here, the group is assumed to live in the home sort. We have a similar result in pure algebraically closed valued fields of positive characteristic, under the additional assumption that the definable group is a subgroup of a linear algebraic group.
Keywords
Cite
@article{arxiv.2601.08423,
title = {On simple groups definable in some valued fields},
author = {Jakub Gismatullin and Immanuel Halupczok and Dugald Macpherson},
journal= {arXiv preprint arXiv:2601.08423},
year = {2026}
}