The Gross-Zagier-Zhang formula over function fields

DOI10.1007/S00208-021-02289-1arXiv1903.02092MaRDI QIDQ6315115

Publication date: 5 March 2019

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.

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Modular forms associated to Drinfel'd modules (11F52) Drinfel'd modules; higher-dimensional motives, etc. (11G09)

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