ON THE BEILINSON-BLOCH-KATO CONJECTURE FOR RANKIN-SELBERG MOTIVES
Résumé
In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value of the Rankin-Selberg L-function does not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch-Kato Selmer group constructed from certain diagonal cycle does not vanish, which is conjec-turally equivalent to the nonvanishing of the central critical first derivative of the Rankin-Selberg L-function, then the Bloch-Kato Selmer group is of rank one.
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