On simple groups definable in some valued fields
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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Rings
Modules
and Algebras
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- HAL (Le Centre pour la Communication Scientifique Directe)
- Publication date
- 13 January 2026
- Language
- EN
- Document type
- Preprint