Séminaires : Séminaire Théorie des Nombres

Equipe(s) : fa, tn, tga,
Responsables :Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel
Email des responsables : cathy.swaenepoel@imj-prg.fr
Salle :
Adresse :



Orateur(s) Olivier de Gaay Fortman - ,
Titre The p-part of BSD for rational elliptic curves at Eisenstein primes
Horaire14:00 à 15:00
RésumeLet 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 give a general introduction to Iwasawa theory and 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 some cases of the p-part of the Birch--Swinnerton-Dyer formula for elliptic curves as above. In particular, for p=3, we obtain improvements on the best known results towards Goldfeld’s conjecture on quadratic twists for elliptic curves with a rational 3-isogeny.
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