Superelliptic degree sets over Henselian fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918218157785088 |
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| author | Galarraga, Alexander Wang, Alexander |
| author_facet | Galarraga, Alexander Wang, Alexander |
| contents | Let $K$ be a discretely valued Henselian field. Creutz and Viray show that the degree set of a curve $C$ over a $p$-adic field can miss infinitely many multiples of the index of $C$, a phenomenon that cannot occur over finitely generated fields. For curves $C/K$ with a cyclic cover of $\mathbb{P}^1$ of prime degree, under mild assumptions, we completely characterize how and when this behavior can occur, and give a method for computing degree sets of curves of this type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superelliptic degree sets over Henselian fields Galarraga, Alexander Wang, Alexander Number Theory Algebraic Geometry Primary: 14G05, 11G20. Secondary: 14G20 Let $K$ be a discretely valued Henselian field. Creutz and Viray show that the degree set of a curve $C$ over a $p$-adic field can miss infinitely many multiples of the index of $C$, a phenomenon that cannot occur over finitely generated fields. For curves $C/K$ with a cyclic cover of $\mathbb{P}^1$ of prime degree, under mild assumptions, we completely characterize how and when this behavior can occur, and give a method for computing degree sets of curves of this type. |
| title | Superelliptic degree sets over Henselian fields |
| topic | Number Theory Algebraic Geometry Primary: 14G05, 11G20. Secondary: 14G20 |
| url | https://arxiv.org/abs/2511.15951 |