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 a 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 explain our strategy and 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.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)