Fourier–Jacobi cycles and arithmetic relative trace formula (with an appendix by Chao Li and Yihang Zhu)

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