Work

On Groups and Fields Definable in $1$ -h-minimal Fields

Year: 2024

Type: article

Abstract: We show that an infinite group G definable in a $1$ -h-minimal field admits a strictly K-differentiable structure with respect to which G is a (weak) Lie group, and we show that definable local subgroups sharing the same Lie algebra have the same germ at the identity. We conclude that infinite fields definable in K are definably isomorphic to finite extensions of K and that $1$ -dimensional groups definable in K are finite-by-abelian-by-finite. Along the way, we develop the basic theory of definable weak K-manifolds and definable morphisms between them.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748024000239

Authors: Juan Pablo Acosta López, Assaf Hasson

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: Israel Science Foundation

Award: G1810118578