Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
Salle :
Adresse :
Description

http://www.imj-prg.fr/tn/STN/stnj.html

 


Orateur(s) K. Rubin - Irvine,
Titre Growth of Selmer groups in generalized dihedral extensions
Date26/06/2006
Horaire14:00 à 15:00
Diffusion
Résume

In joint work with Barry Mazur, we obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields. If F/k is a dihedral extension of number fields of degree 2n with n odd, and E is an elliptic curve over k that has odd rank over the quadratic extension K of k in F, then standard conjectures (and a root number calculation) predict that E(F) has rank at least n. The only case where one can presently prove anything close to this bound is when K is imaginary quadratic, and E(F) contains Heegner points. Mazur and I prove unconditionally that if n is a power of an odd prime p, F/K is unramified at all primes where E has bad reduction, all primes above p split in K/k, and the p-Selmer corank of E/K is odd, then the p-Selmer corank of E/F is at least n. This provides a large class of examples of Z_p^d-extensions where the Selmer module is not a torsion Iwasawa module.

Salle
Adresse
© IMJ-PRG