| ABSTRACT |
In the early 2000s, Greenberg-Vatsal introduced a method for studying the cyclotomic Iwasawa theory of elliptic curves E over Q at Eisenstein primes (i.e., primes p for which E admits a rational p-isogeny). Combined with Kato's work, their method yields important results towards the Birch and Swinnerton-Dyer conjecture in rank 0 (p-converse, p-part of BSD formula). In these talks, I will explain recent joint work with G. Grossi, J. Lee, and C. Skinner in which we develop the method of Greenberg-Vatsal in the anticyclotomic setting, leading to new applications towards the Birch and Swinnerton-Dyer conjecture in rank 1. If time permits, I will also discuss progress towards extending some of these results to small primes. (This is the continuation of the first talk.) |
