A McKay Correspondence in Positive Characteristic
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910736363552768 |
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| author | Liedtke, Christian |
| author_facet | Liedtke, Christian |
| 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2207_06286 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A McKay Correspondence in Positive Characteristic Liedtke, Christian Algebraic Geometry Commutative Algebra Representation Theory 14E16, 14L15, 16T05, 14J17, 13A35, 20C20 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. |
| title | A McKay Correspondence in Positive Characteristic |
| topic | Algebraic Geometry Commutative Algebra Representation Theory 14E16, 14L15, 16T05, 14J17, 13A35, 20C20 |
| url | https://arxiv.org/abs/2207.06286 |