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

 Orateur(s) Adebisi Agboola - , Titre Restricted Selmer groups and special values of p-adic L-functions Date 01/02/2010 Horaire 14:00 à 16:00 Diffusion Résume Let $E/Q$ be an elliptic curve with complex multiplication by thering of integers of an imaginary quadratic field $K$. In 1991, bystudying a certain special value of the Katz two-variable $p$-adic $L$-function lying outside the range of $p$-adic interpolation, K. Rubin formulated a $p$-adic variant of the Birch and Swinnerton-Dyer conjecture when $E(K)$ is infinite, and he proved that his conjecture is true for $E(K)$ of rank one. When $E(K)$ is finite, however, the statement of Rubin's original conjecture no longer applies, and the relevant special value of the appropriate $p$-adic $L$-function is equal to zero. We shall explain what happens in this case. We shall also describe what happens in an analogous situation associated to CM modular forms of higher weight. Salle Adresse