Exponents of Jacobians and relative class groups
Abstract
We prove a lower bound for the exponent of the relative class group P i c 0 X 1 / ϕ ∗ P i c 0 X 2 Pic^0 X_1/\phi ^* Pic^0 X_2 for a covering of curves ϕ : X 1 → X 2 \phi \colon X_1 \to X_2 over a finite field F q \mathbb {F}_q . The results improve on the existing best bounds (due to Stichtenoth) in the case X 2 = P 1 X_2=\mathbb {P}^1 , when the relative class group equals the class group of the function field F q ( X 1 ) \mathbb {F}_q(X_1) , and are completely new for the genuinely relative situation.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4619–4629
- Publication date
- 13 May 2026
- Language
- EN