Heights of Kudla-Rapoport divisors and derivatives of -functions

• 成果类型: Article
• 署名作者: Bruinier, Jan Hendrik; Howard, Benjamin; Yang, Tonghai
• 署名单位: Technical University of Darmstadt; Boston College; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0545-9
• 发表日期: 2015
• 页码: 1-95
• 关键词: intersection theory; cycles; VARIETIES; forms

摘要

We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature . We construct an arithmetic theta lift from harmonic Maass forms of weight to the arithmetic Chow group of the integral model of a unitary Shimura variety, by associating to a harmonic Maass form a linear combination of Kudla-Rapoport divisors, equipped with the Green function given by the regularized theta lift of . Our main result is an equality of two complex numbers: (1) the height pairing of the arithmetic theta lift of against a CM cycle, and (2) the central derivative of the convolution -function of a weight cusp form (depending on ) and the theta function of a positive definite hermitian lattice of rank . When specialized to the case , this result can be viewed as a variant of the Gross-Zagier formula for Shimura curves associated to unitary groups of signature . The proof relies on, among other things, a new method for computing improper arithmetic intersections.