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This is a Quantitative Study study.

October 16, 2025Open Access

An arithmetic analog of Klein's classification of finite subgroups of SL₂(C)

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Finiteness results for finite subgroup schemes of SL2 were established, providing a clearer understanding of their structure.
The study revealed density results for associated quotient singularities, which has implications for algebraic geometry.
Finite, flat, and linearly reductive subgroup schemes over Spec O_K were thoroughly classified, enhancing the theory of linear algebraic groups.
This work expands Klein's classification approach in the context of arithmetic and algebraic geometry.

Implication

This analysis classifies finite, flat subgroup schemes of SL2 over number fields, revealing density in quotient singularities.

Abstract

Let K be a number field with ring of integers OK. We describe and classify finite, flat, and linearly reductive subgroup schemes of SL₂ over Spec\:OK. We also establish finiteness results for these group schemes, as well as density results for the associated quotient singularities.

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Cite This Study

Liedtke et al. (2025) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06e7e2 https://doi.org/10.48550/arxiv.2506.21210

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Implication

This analysis classifies finite, flat subgroup schemes of SL2 over number fields, revealing density in quotient singularities.

An arithmetic analog of Klein's classification of finite subgroups of SL₂(C)

Key Points

Implication

Abstract

Discussion

Cite This Study

An arithmetic analog of Klein's classification of finite subgroups of SL₂(C)

Key Points

Implication

Abstract

Discussion

Cite This Study

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