Fourier-Jacobi圈与算术相对迹公式（附李超、朱一航附录）
Fourier-Jacobi cycles and arithmetic relative trace formula (with an appendix by Chao Li and Yihang Zhu)
摘要：
本文给出了一对等秩酉群的Fourier-Jacobi周期积分的算术模拟。构造了酉志村簇和阿贝尔簇的乘积上的代数圈，即所谓的Fourier-Jacobi圈。我们提出了这类圈的算术GAN-Prasad猜想，该猜想与某些Rankin-Selberg $L$ -函数的中心导数有关，并发展了一个关于该猜想的相对迹公式方法.作为必要的组成部分，我们提出了相应的算术基本引理的猜想，并证实了它的酉群的秩至多为2和极小的情况。
英文摘要：
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 central derivatives of certain Rankin--Selberg $L$-functions, and develop a relative trace formula approach toward this conjecture. As a necessary ingredient, we propose the conjecture of the corresponding arithmetic fundamental lemma, and confirm it for unitary groups of rank at most two and for the minuscule case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
