Faltings heights of CM cycles and derivatives of L-functions

• 成果类型: Article
• 署名作者: Bruinier, Jan Hendrik; Yang, Tonghai
• 署名单位: Technical University of Darmstadt; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0192-8
• 发表日期: 2009
• 页码: 631-681
• 关键词: heegner points; fourier coefficients; elliptic-curves; modular-forms; intersection; THEOREM; jacobi

摘要

We study the Faltings height pairing of arithmetic special divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedean contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a Rankin L-function. We prove the conjecture in certain cases where the Shimura variety has dimension 0, 1, or 2. In particular, we obtain a new proof of the Gross-Zagier formula.