Equivariant splitting of the Hodge–de Rham exact sequence

Abstract Let X be an algebraic curve with a faithful action of finite group G over field k . We show that if the Hodge–de Rham short exact sequence splits -equivariantly then on is weakly ramified. In particular, this generalizes result Köck and Tait for hyperelliptic curves. discuss also converse statements tie problem to lifting coverings curves ring Witt vectors length 2.