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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中文翻译：

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Kudla-Rapoport 循环和局部密度的导数

摘要：我们证明了局部 Kudla-Rapoport 猜想，它是酉 Rapoport-Zink 空间上特殊循环的算术交集数与 Hermitian 形式的局部表示密度导数之间的精确恒等式。作为第一个应用，我们证明了全局 Kudla-Rapoport 猜想，该猜想将酉 Shimura 簇上特殊循环的算术交集数与非相干 Eisenstein 级数的傅立叶系数的中心导数联系起来。结合 Liu 和 Garcia-Sankaran 之前的结果，我们还证明了算术 Siegel-Weil 公式在任何维度上的情况。

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