Faltings heights of abelian varieties with complex multiplication

• 成果类型: Article
• 署名作者: Andreatta, Fabrizio; Goren, Eyal Z.; Howard, Benjamin; Pera, Keerthi Madapusi
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.187.2.3
• 发表日期: 2018
• 页码: 391-531
• 关键词: integral canonical models; shimura varieties; eisenstein series; automorphic-forms; derivatives; REPRESENTATIONS; pairings; cycles

摘要

Let M be the Shimura variety associated with the group of spinor similitudes of a quadratic space over Q of signature (n, 2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special divisors and big CM points on M to the central derivatives of certain L-functions. As an application of this result, we prove an averaged version of Colmez's conjecture on the Faltings heights of CM abelian varieties.