Contents Online
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
DOI: https://dx.doi.org/10.4310/CJM.2021.v9.n1.a1
Authors
Abstract
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