The Gross-Zagier-Zhang formula over function fields
Number Theory
2022-07-07 v4
Abstract
We prove the Gross-Zagier-Zhang formula over global function fields of arbitrary characteristics. It is an explicit formula which relates the Neron-Tate heights of CM points on abelian varieties and central derivatives of associated quadratic base change -functions. Our proof is based on an arithmetic variant of a relative trace identity of Jacquet. This approach is proposed by W. Zhang.
Cite
@article{arxiv.1903.02092,
title = {The Gross-Zagier-Zhang formula over function fields},
author = {Congling Qiu},
journal= {arXiv preprint arXiv:1903.02092},
year = {2022}
}
Comments
85 pages