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

Lifting subgroups of PSL₂ to SL₂ over local fields

Naomi Andrew , Matthew J. Conder , Ari Markowitz , Jeroen Schillewaert This is my paper

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classification math.GR math.NT
keywords mathrmliftedliftinglocalsubgroupsalwaysbrieflycannot
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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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