Equivariant splitting of the Hodge--de Rham exact sequence

Jędrzej Garnek

Equivariant splitting of the Hodge--de Rham exact sequence

Algebraic Geometry 2020-02-20 v2 Number Theory

Authors: Jędrzej Garnek

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 $2$ .

Keywords

algebraic curve finite group action hodge-de rham sequence equivariant splitting weakly ramified witt vectors curve covering

Cite

@article{arxiv.1904.05074,
  title  = {Equivariant splitting of the Hodge--de Rham exact sequence},
  author = {Jędrzej Garnek},
  journal= {arXiv preprint arXiv:1904.05074},
  year   = {2020}
}

Comments

28 pages. Corrected Theorem 1.4 and Subsection 5.3

Equivariant splitting of the Hodge--de Rham exact sequence

Abstract

Keywords

Cite

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