The p-part of BSD for residually reducible elliptic curves of rank one

par Giada Grossi (UCL)

jeudi 23 janv. 2020, 14:00 → 15:00 Europe/Paris

Salle M7 (UMPA, ENS de Lyon)

Let E be an elliptic curve over the rationals and p a prime such that E admits a rational p-isogeny satisfying some assumptions. In a joint work with J. Lee and C. Skinner, we prove the anticyclotomic Iwasawa main conjecture for E/K for some suitable quadratic imaginary field K. I will explain our strategy and how this, combined with complex and p-adic Gross-Zagier formulae, allows us to prove that if E has rank one, then the p-part of the Birch and Swinnerton-Dyer formula for E/Q holds true.