The p-part of BSD for rational elliptic curves at Eisenstein primes

Abstract: Let $E$ be an elliptic curve over the rationals and $p$ an odd prime such that E admits a rational $p$-isogeny satisfying some assumptions. In joint work with F. Castella, J. Lee, and C. Skinner, we study the anticyclotomic Iwasawa theory for $E/K$ for some suitable quadratic imaginary field $K$. I will give a general introduction to Iwasawa theory and to how it can be used to obtain results about the Birch--Swinnerton-Dyer conjecture. In particular, I will talk about how our results, combined with complex and $p$-adic Gross-Zagier formulae, allow us to prove a $p$-converse to the theorem of Gross--Zagier and Kolyvagin and the $p$-part of the Birch--Swinnerton-Dyer formula in analytic rank 1 for elliptic curves as above.

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