Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Francesco Lemma
Email des responsables : alexis.bouthier@imj-prg.fr, francesco.lemma(at)imj-prg.fr
Salle :
Adresse :

Orateur(s) Ben HOWARD - Boston College,
Titre Variation of Heegner points in Hida families.
Horaire14:00 à 15:00
RésumeIf $E$ is an elliptic curve over the rational numbers then one may construct classes in the cohomology of the $p$-adic Tate module $T_p(E)$ by taking the Kummer images of Heegner points. I will describe the construction of a family of Big Heegner points which lift these classes from the cohomology of $T_p(E)$ to the cohomology of Hida's universal ordinary deformation. I will then discuss results and conjectures concerning the nonvanishing of these classes, and applications to Greenberg's conjecture on the generic ranks of Selmer groups in Hida families.