The Gross-Zagier-Zhang formula over function fields

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.

85 pages

References in corpus (6)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• On the arithmetic transfer conjecture for exotic smooth formal moduli spaces
• Comparison of local spherical characters and the Ichino-Ikeda conjecture for unitary groups
• Arithmetic diagonal cycles on unitary Shimura varieties
• Twists of Drinfeld-Stuhler modular varieties
• Shtukas and the Taylor expansion of $L$-functions

Cited by in corpus (1)

• Modularity and Heights of CM cycles on Kuga-Sato varieties