$p$-group Galois covers of curves in characteristic $p$ II
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914999825334272 |
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| author | Garnek, Jędrzej |
| author_facet | Garnek, Jędrzej |
| contents | 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 a $G$-cover of the projective line ramified only over $\infty$ to every $k$-linear action of $G$ on $k[[t]]$. In this paper we relate the HKG-covers to the classical problem of determining the equivariant structure of cohomologies of a curve with an action of a $p$-group. To this end, we present a new way of computing cohomologies of HKG-covers. As an application of our results, we compute the equivariant structure of the de Rham cohomology of Klein four covers in characteristic $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13290 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $p$-group Galois covers of curves in characteristic $p$ II Garnek, Jędrzej Algebraic Geometry Number Theory 14F40, 14G17, 14H30 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 a $G$-cover of the projective line ramified only over $\infty$ to every $k$-linear action of $G$ on $k[[t]]$. In this paper we relate the HKG-covers to the classical problem of determining the equivariant structure of cohomologies of a curve with an action of a $p$-group. To this end, we present a new way of computing cohomologies of HKG-covers. As an application of our results, we compute the equivariant structure of the de Rham cohomology of Klein four covers in characteristic $2$. |
| title | $p$-group Galois covers of curves in characteristic $p$ II |
| topic | Algebraic Geometry Number Theory 14F40, 14G17, 14H30 |
| url | https://arxiv.org/abs/2308.13290 |