Iwasawa theory of elliptic curves at Eisenstein primes

Abstract: In an influential paper from 2000, Greenberg and 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 results had important implications towards the Birch and Swinnerton-Dyer conjecture in rank 0. In this talk, I will try to convey the main ideas of their method, and then move on to explain recent joint work with G. Grossi and C. Skinner (partly in progress) in which we develop the method of Greenberg-Vatsal in the anti-cyclotomic setting, leading to new applications towards the Birch and Swinnerton-Dyer conjecture in rank 1.

number theory

Audience: researchers in the discipline

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11