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

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.

43 pages, comments welcome!