We study the resurgence structure of a formal normalization of a certain vector field to the normal form using “mould calculus” developed by J. Écalle. We also describe the resurgence structure of transseries solutions of a nonlinear ordinary differential equation.

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.