Cyclic covers of an algebraic curve from an Adelic viewpoint
Abstract
We propose an algebraic method for the classification of branched Galois covers of a curve \(X\), focused on studying Galois ring extensions of its geometric adele ring \(\mathbb{A}_{X}\). As an application, we deal with cyclic covers; namely, we determine when a given cyclic ring extension of \(\mathbb{A}_{X}\) comes from a corresponding cover of curves \(Y\) → \(X\), which is reminiscent of a Grunwald-Wang problem, and also determine when two covers yield isomorphic ring extensions, which is known in the literature as an equivalence problem. This completely algebraic method permits us to recover ramification, certain analytic data such as rotation numbers, and enumeration formulas for covers.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Differential Equations and Dynamical Systems
Meromorphic and Entire Functions
Publication details
- Journal / source
- Cubo
- Publisher
- Universidad de La Frontera
- Volume
- 28
- Issue
- 2
- Pages
- 261–261
- Publication date
- 14 May 2026
- Language
- EN