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arXiv · 1904.05074

Equivariant splitting of the Hodge--de Rham exact sequence

Jędrzej Garnek
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Abstract

Let $X$ be an algebraic curve with an 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 K\"{o}ck 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 $2$.

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Jędrzej Garnek. 2019-04-10. Equivariant splitting of the Hodge--de Rham exact sequence. https://arxiv.org/abs/1904.05074

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