Euler characteristic of crepant resolutions of specific modular quotient singularities

Abstract: In this paper, we consider a generalization of McKay correspondence in positive characteristic regarding Euler characteristic of crepant resolutions given by finite subgroups of the special linear group. As the main result, we prove that the generalization holds for groups with a specific semidirect product structure. Apart from such groups, two certain examples for groups with more difficult structure are also given.