Euler characteristic of crepant resolutions of specific modular quotient singularities

Abstract

In this paper, we consider a generalization of the McKay correspondence in positive characteristic regarding the Euler characteristic of crepant resolutions of quotient singularities given by finite subgroups of the special linear group. As the main result, we prove that this generalization holds for groups with a specific semidirect product structure, using the wild McKay correspondence over finite fields as mass formulas. Furthermore, two additional examples with more complicated structures are also given. Based on our main result, we propose a conjectural form of the generalized McKay correspondence in the modular case.

arXiv comment24 pages

References in corpus (6)

• The $p$-cyclic McKay correspondence via motivic integration
• The wild McKay correspondence and $p$-adic measures
• Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions
• Toward motivic integration over wild Deligne-Mumford stacks
• Modular quotient varieties and singularities by the cyclic group of order $2p$
• Crepant resolution of ${\mathbb{A}}^4/A_4$ in characteristic 2