Selmer groups, automorphic periods, and Bloch-Kato Conjecture

Joint IAS/Princeton University Number Theory Seminar
Topic:Selmer groups, automorphic periods, and Bloch-Kato Conjecture
Speaker:Yifeng Liu
Affiliation:Massachusetts Institute of Technology
Date:Thursday, December 11
Time/Room:4:30pm - 5:30pm/Fine 214, Princeton University

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.