On the arithmetic Siegel-Weil formula for GSpin Shimura varieties

• 成果类型: Article
• 署名作者: Li, Chao; Zhang, Wei
• 署名单位: Columbia University; Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01106-z
• 发表日期: 2022
• 页码: 1353-1460
• 关键词: integral canonical models; special cycles; derivatives; REPRESENTATION; intersection

摘要

We formulate and prove a local arithmetic Siegel-Weil formula for GSpin Rapoport-Zink spaces, which is a precise identity between the arithmetic intersection numbers of special cycles on GSpin Rapoport-Zink spaces and the derivatives of local representation densities of quadratic forms. As a first application, we prove a semi-global arithmetic Siegel-Weil formula as conjectured by Kudla, which relates the arithmetic intersection numbers of special cycles on GSpin Shimura varieties at a place of good reduction and the central derivatives of nonsingular Fourier coefficients of incoherent Siegel Eisenstein series.