English

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 LL-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

R2 v1 2026-06-23T07:59:14.282Z