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

2021/03/21 by Tony Feng, Feng, Tony, Zhiwei Yun +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2103.11514

openalex publication_date 2021/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th 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 unitary 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.

Citations

• Kudla--Rapoport cycles and derivatives of local densities

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