Kudla--Rapoport cycles and derivatives of local densities

Chao Li; Wei Zhang

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arXiv · 1908.01701

Kudla--Rapoport cycles and derivatives of local densities

Chao Li·Wei Zhang

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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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Chao Li, Wei Zhang. 2019-08-05. Kudla--Rapoport cycles and derivatives of local densities. https://arxiv.org/abs/1908.01701

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