Equivariant splitting of the Hodge–de Rham exact sequence

Abstract

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

𝑝-group Galois covers of curves in characteristic 𝑝

“…Then π is unramified outside of {Q 1 , Q 2 }, since those are the only poles of h 0 and h 1 , and is in standard form at Q 1 and at Q 2 . Hence, since ord (9,15).…”