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) A. Agashé - ,
Titre On invisible elements of the Tate-Shafarevich group.
Date07/01/1999
Horaire14:00 à 16:00
Diffusion
RésumeLet $J$ 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.
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