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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.21210 |
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| _version_ | 1866908423580286976 |
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| author | Liedtke, Christian Satriano, Matthew |
| author_facet | Liedtke, Christian Satriano, Matthew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An arithmetic analog of Klein's classification of finite subgroups of $\mathrm{SL}_2(\mathbb{C})$ Liedtke, Christian Satriano, Matthew Algebraic Geometry Number Theory 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. |
| title | An arithmetic analog of Klein's classification of finite subgroups of $\mathrm{SL}_2(\mathbb{C})$ |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2506.21210 |