A McKay Correspondence in Positive Characteristic
We establish a McKay correspondence for finite and linearly reductive subgroup schemes of ${\mathbf {SL}}_2$ in positive characteristic. As an application, we obtain a McKay correspondence for all rational double point singularities in characteristic $p\geq 7$ . We discuss linearly redu...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424000987/type/journal_article |
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| Summary: | We establish a McKay correspondence for finite and linearly reductive subgroup schemes of
${\mathbf {SL}}_2$
in positive characteristic. As an application, we obtain a McKay correspondence for all rational double point singularities in characteristic
$p\geq 7$
. 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. |
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| ISSN: | 2050-5094 |