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arXiv · 2506.21210

An arithmetic analog of Klein's classification of finite subgroups of $\mathrm{SL}_2(\mathbb{C})$

Christian Liedtke·Matthew Satriano
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Abstract

Let $K$ be a number field with ring of integers $\mathcal{O}_K$. We describe and classify finite, flat, and linearly reductive subgroup schemes of $\mathrm{SL}_2$ over $\mathrm{Spec}\:\mathcal{O}_K$. We also establish finiteness results for these group schemes, as well as density results for the associated quotient singularities.

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Christian Liedtke, Matthew Satriano. 2025-06-26. An arithmetic analog of Klein's classification of finite subgroups of $\mathrm{SL}_2(\mathbb{C})$. https://arxiv.org/abs/2506.21210

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