| Résume | Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a finite $p$-group. The results of Harbater, Katz and Gabber associate to every action of $G$ on $k[[t]]$ a $G$-cover of the projective line ramified only over $\infty$. During this talk we will present a new way of computing cohomologies of HKG-covers. We apply this result to the classical problem of determining the equivariant structure of cohomologies of a curve with an action of a $p$-group. As an example, we compute the de Rham cohomology of Klein four covers. |
