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Hauptverfasser: Galarraga, Alexander, Wang, Alexander
Format: Preprint
Veröffentlicht: 2025
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Online-Zugang:https://arxiv.org/abs/2511.15951
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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