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arXiv · 2412.12467

Bounds for the relative class number problem for function fields

Santiago Arango-Piñeros·María Chara·Asimina S. Hamakiotes·Kiran S. Kedlaya·Gustavo Rama
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Abstract

We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the relative class number two problem in all cases where the base field has constant field not equal to $\mathbb{F}_2$.

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Santiago Arango-Piñeros, María Chara, Asimina S. Hamakiotes, Kiran S. Kedlaya, Gustavo Rama. 2025-05-23. Bounds for the relative class number problem for function fields. https://arxiv.org/abs/2412.12467

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