Gardado en:
| Autor Principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2207.06286 |
| Tags: |
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Table of Contents:
- We establish a McKay correspondence for finite and linearly reductive subgroup schemes of $\mathrm{SL}_2$ in positive characteristic. As an application, we obtain a McKay correspondence for all rational double point singularities in characteristic $p\geq7$. We discuss linearly reductive quotient singularities and canonical lifts over the ring of Witt vectors. In dimension 2, we establish simultaneous resolutions of singularities of these canonical lifts via $G$-Hilbert schemes. In the appendix, we discuss several approaches towards the notion of conjugacy classes for finite group schemes: This is an ingredient in McKay correspondences, but also of independent interest.