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 contents of this conjecture and stating its asymptotic variant. As time permits, I will sketch a proof of the asymptotic BSD for CM elliptic curves, which relies on the Iwasawa theoretic study of the Kato-Beilinson elements and the reciprocity law that relates them to relevant L-functions.