English

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

Algebraic Geometry 2025-06-27 v1 Number Theory

Abstract

Let KK be a number field with ring of integers OK\mathcal{O}_K. We describe and classify finite, flat, and linearly reductive subgroup schemes of SL2\mathrm{SL}_2 over SpecOK\mathrm{Spec}\:\mathcal{O}_K. We also establish finiteness results for these group schemes, as well as density results for the associated quotient singularities.

Keywords

Cite

@article{arxiv.2506.21210,
  title  = {An arithmetic analog of Klein's classification of finite subgroups of $\mathrm{SL}_2(\mathbb{C})$},
  author = {Christian Liedtke and Matthew Satriano},
  journal= {arXiv preprint arXiv:2506.21210},
  year   = {2025}
}

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43 pages, comments welcome!