The authors prove the local and global Kudla-Rapoport conjectures and, combining with results of Liu and Garcia-Sankaran, the arithmetic Siegel-Weil formula in arbitrary dimension.
A reformulation of the Siegel series and intersection numbers
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abstract
In this paper, we will explain a conceptual reformulation and inductive formula of the Siegel series. Using this, we will explain that both sides of the local intersection multiplicities of [GK93] and the Siegel series have the same inherent structures, beyond matching values. As an application, we will prove a new identity between the intersection number of two modular correspondences over Fp and the sum of the Fourier coefficients of the Siegel-Eisenstein series for Sp_4 of weight 2, which is independent of p (> 2). In addition, we will explain a description of the local intersection multiplicities of the special cycles over F_p on the supersingular locus of the `special fiber' of the Shimura varieties for GSpin(n; 2), n<=3 in terms of the Siegel series directly.
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2019 1verdicts
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Kudla--Rapoport cycles and derivatives of local densities
The authors prove the local and global Kudla-Rapoport conjectures and, combining with results of Liu and Garcia-Sankaran, the arithmetic Siegel-Weil formula in arbitrary dimension.