Iwasawa's main conjecture for Rankin--Selberg motives in the anticyclotomic case

In this article, we study the Iwasawa theory for cuspidal automorphic representations of GL (n) (n+1) over CM fields along anticyclotomic directions, in the framework of the Gan--Gross--Prasad conjecture for unitary groups. We prove one-side divisibility of the corresponding Iwasawa main conjecture: when the global root number is 1, the p-adic L-function belongs to the characteristic ideal of the Iwasawa Bloch--Kato Selmer group; when the global root number is -1, the square of the characteristic ideal of a certain Iwasawa module is contained in the characteristic ideal of the torsion part of the Iwasawa Bloch--Kato Selmer group (analogous to Perrin-Riou's Heegner point main conjecture).