turkmath.org

The conjecture of Birch and Swinnerton-Dyer (BSD) is one of the Clay Millennium problems that links the arithmetic invariants of an elliptic curve to its analytic invariants. Most of this talk will be devoted to explaining the content of this conjecture and stating an *asymptotic* variant. As time permits, I will sketch a proof of this asymptotic BSD conjecture for CM elliptic curves (and more generally, for CM elliptic modular forms) along the anticyclotomic tower. The proof relies on the Iwasawa theoretic study of the Beilinson-Kato elements and a reciprocity law that relates them to relevant L-functions.