Hall 123

Elliptic Cruves and the Birch and Swinnerton-Dyer Conjecture

Florian Sprung

Arizona State University

The Birch and Swinnerton-Dyer conjecture, one of the millenium problems, is a bridge between algebraic invariants of an elliptic curve and its (complex analytic) L-function. In the case of low ranks, a lot is known thanks to works going back to Coates/Wiles. The full conjecture can be proved up to the finitely many bad primes and the prime 2, by proving the Iwasawa main conjecture. This talk assumes no specialized background in number theory.