Riemann-Hurwitz Formula for Arithmetic Surfaces
Algebraic Geometry
2025-12-04 v2
Abstract
In this paper, we presents a method for factoring morphisms between arithmetic surfaces based on the regularity of arithmetic surfaces. Using this factorization, we derive a Riemann-Hurwitz formula satisfied by the ramification divisor and the canonical divisor on arithmetic surfaces. We also extend this formula to Arakelov theory.
Cite
@article{arxiv.2510.08033,
title = {Riemann-Hurwitz Formula for Arithmetic Surfaces},
author = {Ziyang Zhu},
journal= {arXiv preprint arXiv:2510.08033},
year = {2025}
}
Comments
14 pages, we have corrected some errors from the previous version, comments welcome!