Open subgroups of $p$-adic algebraic groups

Anand Pillay; Ningyuan Yao

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arXiv · 2304.14798

Open subgroups of $p$-adic algebraic groups

Anand Pillay·Ningyuan Yao

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Abstract

In \cite{Pillay} and more formally in \cite{Onshuus-Pillay} it was asked whether open subgroups of $p$-adic algebraic groups are ($p$-adic) semialgebraic, equivalently, definable in the structure $(\mathbb Q_{p}, +, \times)$. We give a positive answer in the commutative case. Together with results of \cite{Prasad} this leads to a positive answer for reductive algebraic groups.

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BibTeX RIS

Anand Pillay, Ningyuan Yao. 2023-04-28. Open subgroups of $p$-adic algebraic groups. https://arxiv.org/abs/2304.14798

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