An interplay between the p-parts of the Tate-Shafarevich group

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• Vladimir Dokchitser (Warwick University)
• Tuesday 28 April 2015, 16:15-17:15
• MR13.

If you have a question about this talk, please contact Jack Thorne.

I will discuss what happens when one combines the Birch—Swinnerton-Dyer conjecture together with Deligne’s conjecture on Galois equivariance of L-values. As an example, I will exhibit a family of elliptic curves over a number field which conjecturally cannot have Sha of order p squared (for a suitably chosen prime p), but can have Sha of order p squared * something coprime to p—a phenomenon that cannot be detected when restricting attention to the p-Selmer group alone. I plan to discuss some other examples of this nature as well.

This talk is part of the Number Theory Seminar series.

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