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

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arxiv 2401.05192 v2 pith:O5WFPNRW submitted 2024-01-10 math.GR math.NT

Naomi Andrew , Matthew J. Conder , Ari Markowitz , Jeroen Schillewaert This is my paper · ORCID
classification math.GRmath.NT
keywords mathrmliftedliftinglocalsubgroupsalwaysbrieflycannot
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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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