Kudla–Rapoport cycles and derivatives of local densities

Li, Chao; Zhang, Wei

doi:10.1090/jams/988

Kudla–Rapoport cycles and derivatives of local densities
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by Chao Li and Wei Zhang

J. Amer. Math. Soc. 35 (2022), 705-797

DOI: https://doi.org/10.1090/jams/988

Published electronically: September 10, 2021

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Abstract:

We prove the local Kudla–Rapoport conjecture, which is a precise identity between the arithmetic intersection numbers of special cycles on unitary Rapoport–Zink spaces and the derivatives of local representation densities of hermitian forms. As a first application, we prove the global Kudla–Rapoport conjecture, which relates the arithmetic intersection numbers of special cycles on unitary Shimura varieties and the central derivatives of the Fourier coefficients of incoherent Eisenstein series. Combining previous results of Liu and Garcia–Sankaran, we also prove cases of the arithmetic Siegel–Weil formula in any dimension.

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