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arXiv · 1903.02092

The Gross-Zagier-Zhang formula over function fields

Congling Qiu
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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 $L$-functions. Our proof is based on an arithmetic variant of a relative trace identity of Jacquet. This approach is proposed by W. Zhang.

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Congling Qiu. 2019-03-05. The Gross-Zagier-Zhang formula over function fields. https://arxiv.org/abs/1903.02092

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