A proof of the Kudla-Rapoport conjecture for Kramer models

• 成果类型: Article
• 署名作者: He, Qiao; Li, Chao; Shi, Yousheng; Yang, Tonghai
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Columbia University; Zhejiang University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01209-1
• 发表日期: 2023
• 页码: 721-817
• 关键词: l-derivatives; unitary

摘要

We prove the Kudla-Rapoport conjecture for Kramer models of unitary Rapoport-Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kramer models and modified derived local densities of hermitian forms. As an application, we relax the local assumptions at ramified places in the arithmetic Siegel-Weil formula for unitary Shimura varieties, which is in particular applicable to unitary Shimura varieties associated to unimodular hermitian lattices over imaginary quadratic fields.