On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives

In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to Rankin–Selberg products of conjugate self-dual automorphic representations, within framework Gan–Gross–Prasad conjecture. We show that if central critical value L-function does not vanish, then Bloch–Kato Selmer group with coefficients in a favorable field corresponding motive vanishes. also class constructed from certain diagonal cycle which is conjecturally equivalent nonvanishing first derivative L-function, rank one.