Year: 2025
Type: preprint
Abstract: 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).
Source: arXiv (Cornell University)
Author: Sajadi, Fateme
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417267352
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