# 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) A. Agashé - , Titre On invisible elements of the Tate-Shafarevich group. Date 07/01/1999 Horaire 14:00 à 16:00 Diffusion Résume Let $J$ be an abelian variety and $A$ be any sub-abelian variety of$J$, both defined over $\Q$. An element of the Tate-Shafarevich group of$A$ is said to be visible in $J$ if the corresponding torsor is isomorphicover $\Q$ to a subvariety of $J$. This concept was introduced byMazur in the context of optimal modular elliptic curves. We show, basedon calculations, assuming the Birch-Swinnerton-Dyer conjecture, that thereare elements of the Tate-Shafarevich group of certain sub-abelian varieitiesof $J_0(p)$ and $J_1(p)$ that are not visible. Salle Adresse