Complex multiplication cycles and Kudla-Rapoport divisors

• 成果类型: Article
• 署名作者: Howard, Benjamin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.176.2.9
• 发表日期: 2012
• 页码: 1097-1171
• 关键词: arithmetic intersection theory; quasi-canonical liftings; borcherds products; eisenstein series; algebraic stacks; modular surfaces; heegner points; derivatives; VARIETIES; SPACES

摘要

We study the intersections of special cycles on a unitary Shimura variety of signature (n - 1, 1) and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of conjectures of Kudla and suggest a Gross-Zagier theorem for unitary Shimura varieties.