Work

Definably semisimple groups interpretable in $p$-adically closed fields

Year: 2022

Type: preprint

Abstract: Let $K$ be a $p$-adically closed field and $G$ a group interpretable in $K$. We show that if $G$ is definably semisimple (i.e. $G$ has no definable infinite normal abelian subgroups) then there exists a finite normal subgroup $H$ such that $G/H$ is definably isomorphic to a $K$-linear group. The result remains true in models of $\mathrm{Th}(\mathbb{Q}_p^{an})$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2211.00141

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

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4308015261

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