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
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Orateur(s) Adebisi Agboola - ,
Titre Restricted Selmer groups and special values of p-adic L-functions
Date01/02/2010
Horaire14:00 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.
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