In this article, we develop an arithmetic analogue of Fourier–Jacobi period integrals for a pair of unitary groups of equal rank. We construct the so-called Fourier–Jacobi cycles, which are algebraic cycles on the product of unitary Shimura varieties and abelian varieties.We propose the arithmetic Gan–Gross–Prasad conjecture for these cycles, which is related to the central derivatives of certain Rankin–Selberg $L$-functions, and develop a relative trace formula approach toward this conjecture.

中文翻译：

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傅里叶-雅可比循环和算术相对迹公式（附李超和朱一航的附录）

在本文中，我们开发了一对等阶酉群的傅立叶-雅可比周期积分的算术模拟。我们构建了所谓的傅里叶-雅可比循环，它们是关于酉 Shimura 簇和阿贝尔簇的乘积的代数循环。我们提出了这些循环的算术 Gan-Gross-Prasad 猜想，它与某些 Rankin 的中心导数有关–Selberg $L$-函数，并针对该猜想开发了一种相对迹公式方法。