Double-header seminars:  actual time to be determined.  The Bloch-Kato Conjecture, which generalizes the B-SD Conjecture to higher dimensional varieties, predicts a relation between certain Selmer group and L-function. The famous works of Gross-Zagier and Kolyvagin give results for elliptic curves when the analytic rank is at most 1. In this talk, we will discuss new results toward the Conjecture for cases of more complicated motives. We will also discuss how automorphic periods show up in the picture, which is a crucial step in the proof.