Arithmetic theta lifts and the arithmetic Gan–Gross–Prasad conjecture for unitary groups

Abstract

We propose a precise formula relating the height of certain diagonal cycles on the product of unitary Shimura varieties and the central derivative of some tensor product $L$-functions. This can be viewed as a refinement of the arithmetic Gan–Gross–Prasad conjecture. We use the theory of arithmetic theta lifts to prove some endoscopic cases of it for $U(2)\times U(3)$.