The Langlands functoriality conjecture, as reformulated in the “beyond endoscopy” program, predicts comparisons between (stable) trace formulas of different groups G1,G2 for every morphism G1L→LG2 their L-groups. This conjecture can be seen a special case more general which replaces reductive by spherical varieties and formula its generalization, relative formula. goal this article precursor [1...

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 co...