Cambridge Journal of Mathematics

Volume 9 (2021)

Number 1

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

Pages: 1 – 147



Yifeng Liu (Institute for Advanced Study in Mathematics, Zhejiang University, Hangzhou, China)

Yihang Zhu (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Chao Li (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)


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.

2010 Mathematics Subject Classification

11G18, 11G40, 14G40

Received 23 January 2019

Published 27 October 2021