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On rational double points over nonclosed fields

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arxiv 2503.19787 v1 pith:2SUH6GY7 submitted 2025-03-25 math.AG

Christian Liedtke , Matthew Satriano This is my paper · ORCID
classification math.AG
keywords doublefieldsrationalsingularitiesarisecomputedetermineequations
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abstract

We compute the equations of all rational double point singularities and we determine their types over perfect ground fields $k$ that arise as quotient singularities by finite linearly reductive subgroup schemes of $\textrm{SL}_{2,k}$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. McKay correspondence for linearly reductive finite group schemes in positive characteristic

    math.AG 2026-08 accept novelty 7.0 of 10

    Crepant resolutions of quotients by finite linearly reductive group schemes in any characteristic have Euler number equal to the number of irreducible representations of the group.

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

    math.AG 2025-06 conditional novelty 6.0 of 10

    Over rings of integers in number fields, finite flat linearly reductive subgroups of SL2 are exactly fppf local forms of μ_n, with finitely many GL2-conjugacy classes and controlled quotient singularities.

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