The weak Birch and Swinnerton-Dyer conjecture predicts a relation between an algebraic object—the rank of an elliptic curve, with an analytic object—the order of vanishing of its associated L-function at a special point. In this expository talk, I will state Bloch and Kato’s vast generalization of this conjecture and explore the Galois cohomological tools, particularly the Bloch-Kato Selmer groups, that go into the conjecture.
Talk by Ken Willyard.