Geodesic
A McKay Correspondence in Positive Characteristic
Forum of Mathematics, Sigma, Tome 12 (2024)

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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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     author = {Christian Liedtke},
     title = {A {McKay} {Correspondence} in {Positive} {Characteristic}},
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Christian Liedtke. A McKay Correspondence in Positive Characteristic. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.98

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