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

Yatir Halevi; Assaf Hasson; Ya'acov Peterzil

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arXiv · 2211.00141

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

Yatir Halevi·Assaf Hasson·Ya'acov Peterzil

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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 $\mathrm{Th}(\mathbb{Q}_p^{an})$.

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BibTeX RIS

Yatir Halevi, Assaf Hasson, Ya'acov Peterzil. 2022-10-31. Definably semisimple groups interpretable in $p$-adically closed fields. https://arxiv.org/abs/2211.00141

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