Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-covers in characteristic $2$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908829671751680 |
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| author | Booher, Jeremy Groen, Steven R. Kramer-Miller, Joe |
| author_facet | Booher, Jeremy Groen, Steven R. Kramer-Miller, Joe |
| contents | In this article we study the Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-Galois covers $π:Y \to X$ in characteristic two. When the base curve $X$ is ordinary, we show that the Ekedahl-Oort type of $Y$ is completely determined by the genus of $X$ and the ramification of $π$. For a general base curve $X$, we prove bounds on the Ekedahl-Oort depending on the Ekedahl-Oort type of $X$ and the ramification of $π$. Along the way, we develop a theory of \emph{enhanced differentials of the second kind}. This theory allows us to study algebraic de Rham cohomology in any characteristic by working directly with differentials, in contrast to the standard Čech resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-covers in characteristic $2$ Booher, Jeremy Groen, Steven R. Kramer-Miller, Joe Number Theory Algebraic Geometry 11G20, 14H10, 14H30, 14H40, 14F40 (Primary) 14G17, 14L15 (Secondary) In this article we study the Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-Galois covers $π:Y \to X$ in characteristic two. When the base curve $X$ is ordinary, we show that the Ekedahl-Oort type of $Y$ is completely determined by the genus of $X$ and the ramification of $π$. For a general base curve $X$, we prove bounds on the Ekedahl-Oort depending on the Ekedahl-Oort type of $X$ and the ramification of $π$. Along the way, we develop a theory of \emph{enhanced differentials of the second kind}. This theory allows us to study algebraic de Rham cohomology in any characteristic by working directly with differentials, in contrast to the standard Čech resolution. |
| title | Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-covers in characteristic $2$ |
| topic | Number Theory Algebraic Geometry 11G20, 14H10, 14H30, 14H40, 14F40 (Primary) 14G17, 14L15 (Secondary) |
| url | https://arxiv.org/abs/2511.02733 |