On the Arithmetic Gan-Gross-Prasad Conjecture for U(2) x U(3)

Abstract

In its broadest sense, the arithmetic Gan-Gross-Prasad (GGP) Conjecture relates the central value of the derivative of a certain $L$-function to a height pairing of certain algebraic cycles on Shimura varieties. Xue proved the arithmetic GGP conjecture for $\U(2) \times \U(3)$ operating under the assumption that the underlying Shimura varieties are projective as well as some hypotheses on the representations to which the $L$-function in question is attached. Assuming some working hypotheses about arithmetic theta lifting, we extend Xue's work to toroidal compactifications of Shimura varieties through the use of Hecke correspondences to annihilate contributions from the boundary thereby reducing much of the problem to the setting where many of Xue's results apply.