Crepant resolution of $\mathbb{A}^4/A_4$ in characteristic 2

Abstract

In this paper, we construct a crepant resolution for the quotient singularity $\mathbb{A}^4/A_4$ in characteristic 2, where $A_4$ is the alternating group of degree 4 with permutation action on $\mathbb{A}^4$. By computing the Euler number of the crepant resolution, we obtain a new counterexample to an analogous statement of McKay correspondence in positive characteristic.