Modular Heights of Quaternionic Shimura Curves
Number Theory
2024-05-28 v3 Algebraic Geometry
Abstract
The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these works are in turn inspired by the Pioneering work of Gross-Zagier and some philosophies of Kudla's program.
Keywords
Cite
@article{arxiv.2205.13995,
title = {Modular Heights of Quaternionic Shimura Curves},
author = {Xinyi Yuan},
journal= {arXiv preprint arXiv:2205.13995},
year = {2024}
}