Crepant resolution of $\mathbf{A}^{4}/A_{4}$ in characteristic 2

Abstract

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