Higher Siegel-Weil formula for unitary groups: the non-singular terms

• 成果类型: Article
• 署名作者: Feng, Tony; Yun, Zhiwei; Zhang, Wei
• 署名单位: University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01228-y
• 发表日期: 2024
• 页码: 569-668
• 关键词: eisenstein series; Taylor expansion; l-derivatives; shtukas

摘要

We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the rth central derivative of non-singular Fourier coefficients of a normalized Siegel-Eisenstein series, and (2) the degree of special cycles of virtual dimension 0 on the moduli stack of hermitian shtukas with r legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein series.