A Unified Finiteness Theorem For Curves Over Function Fields
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915410696208384 |
|---|---|
| author | Sajadi, Fateme |
| author_facet | Sajadi, Fateme |
| contents | Motivated by the analogy between number fields and function fields, this paper extends the main result of \cite{janbazi2025unified} to the function field setting. Let $C$ be a smooth affine curve over a finite field, and let $π: S \rightarrow C$ be a smooth, proper model of a curve over $C$. Then, for any fixed integer $n \in \mathbb{N}$, there are only finitely many horizontal divisors of degree $n$ that are étale over the base $C$, up to the action of the automorphism group and Frobenius (in the isotrivial case). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Finiteness Theorem For Curves Over Function Fields Sajadi, Fateme Algebraic Geometry Number Theory Motivated by the analogy between number fields and function fields, this paper extends the main result of \cite{janbazi2025unified} to the function field setting. Let $C$ be a smooth affine curve over a finite field, and let $π: S \rightarrow C$ be a smooth, proper model of a curve over $C$. Then, for any fixed integer $n \in \mathbb{N}$, there are only finitely many horizontal divisors of degree $n$ that are étale over the base $C$, up to the action of the automorphism group and Frobenius (in the isotrivial case). |
| title | A Unified Finiteness Theorem For Curves Over Function Fields |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2507.19669 |