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SUMMARY:An interplay between the p-parts of the Tate-Shafarevich group - V
 ladimir Dokchitser (Warwick University)
DTSTART:20150428T151500Z
DTEND:20150428T161500Z
UID:TALK58793@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:I will discuss what happens when one combines the Birch--Swinn
 erton-Dyer conjecture together with Deligne's conjecture on Galois equivar
 iance of L-values. As an example\, I will exhibit a family of elliptic cur
 ves over a number field which conjecturally cannot have Sha of order p squ
 ared (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 res
 tricting attention to the p-Selmer group alone. I plan to discuss some oth
 er examples of this nature as well.
LOCATION:MR13
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