The Gross–Zagier–Zhang formula over function fields

Autor:	Congling Qiu
Rok vydání:	2021
Předmět:	Base change Elliptic curve Pure mathematics Quadratic equation Conjecture Rank (linear algebra) Mathematics::Number Theory General Mathematics Trace identity Function (mathematics) Abelian group Mathematics
Zdroj:	Mathematische Annalen. 384:625-731
ISSN:	1432-1807 0025-5831
DOI:	10.1007/s00208-021-02289-1
Popis:	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 Zhang. We apply our results to the Birch and Swinnerton–Dyer conjecture for abelian varieties of $${\mathrm {GL}}_2$$ -type. In particular, we prove the conjecture for elliptic curves of analytic rank 1.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::501caccc9f1aaf426d34d24c65beb9c5 https://doi.org/10.1007/s00208-021-02289-1 Zobrazit plný text záznamu Full text from SpringerLink