$p$-torsion for unramified Artin--Schreier covers of curves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914913079787520 |
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| author | Cais, Bryden Ulmer, Douglas |
| author_facet | Cais, Bryden Ulmer, Douglas |
| contents | Let $Y\to X$ be an unramified Galois cover of curves over a perfect field $k$ of characteristic $p>0$ with $\mathrm{Gal}(Y/X)\cong\mathbb{Z}/p\mathbb{Z}$, and let $J_X$ and $J_Y$ be the Jacobians of $X$ and $Y$ respectively. We consider the $p$-torsion subgroup schemes $J_X[p]$ and $J_Y[p]$, analyze the Galois-module structure of $J_Y[p]$, and find restrictions this structure imposes on $J_Y[p]$ (for example, as manifested in its Ekedahl--Oort type) taking $J_X[p]$ as given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_16346 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $p$-torsion for unramified Artin--Schreier covers of curves Cais, Bryden Ulmer, Douglas Number Theory Algebraic Geometry 11G20, 14F40, 14H40 (Primary) 11G10, 14G17, 14K15 (Secondary) Let $Y\to X$ be an unramified Galois cover of curves over a perfect field $k$ of characteristic $p>0$ with $\mathrm{Gal}(Y/X)\cong\mathbb{Z}/p\mathbb{Z}$, and let $J_X$ and $J_Y$ be the Jacobians of $X$ and $Y$ respectively. We consider the $p$-torsion subgroup schemes $J_X[p]$ and $J_Y[p]$, analyze the Galois-module structure of $J_Y[p]$, and find restrictions this structure imposes on $J_Y[p]$ (for example, as manifested in its Ekedahl--Oort type) taking $J_X[p]$ as given. |
| title | $p$-torsion for unramified Artin--Schreier covers of curves |
| topic | Number Theory Algebraic Geometry 11G20, 14F40, 14H40 (Primary) 11G10, 14G17, 14K15 (Secondary) |
| url | https://arxiv.org/abs/2307.16346 |