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arXiv · 2401.05192

Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields

Naomi Andrew·Matthew J. Conder·Ari Markowitz·Jeroen Schillewaert
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Abstract

Let $K$ be a non-archimedean local field. We show that discrete subgroups without 2-torsion in $\mathrm{PSL}_2(K)$ can always be lifted to $\mathrm{SL}_2(K)$, and provide examples (when $\mathrm{char}(K) \neq 2$) which cannot be lifted if either of these conditions is removed. We also briefly discuss lifting representations of groups into $\mathrm{PSL}_2(K)$ to $\mathrm{SL}_2(K)$.

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Naomi Andrew, Matthew J. Conder, Ari Markowitz, Jeroen Schillewaert. 2024-01-10. Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields. https://arxiv.org/abs/2401.05192

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