Work

Semisimple groups interpretable in various valued fields

Year: 2025

Type: article

Abstract: We study infinite groups interpretable in power bounded T-convex, V-minimal or p-adically closed fields. We show that if G is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups) then, up to a finite index subgroup, it is definably isogenous to a group $G_1\times G_2$ , where $G_1$ is a K-linear group and $G_2$ is a $\mathbf {k}$ -linear group. The analysis is carried out by studying the interaction of G with four distinguished sorts: the valued field K, the residue field $\mathbf {k}$ , the value group $\Gamma $ , and the closed $0$ -balls $K/\mathcal {O}$ .

Source: Forum of Mathematics Sigma

DOI: 10.1017/fms.2025.10084

Authors: Yatir Halevi, Assaf Hasson, Ya'acov Peterzil

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,650

Funder: Israel Science Foundation

Awards: G1728871502, G1810118578