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SUMMARY:Hasse principle for Kummer varieties (joint work with Yonatan Harp
 az) - Alexei Skorobogatov (Imperial College)
DTSTART:20150120T161500Z
DTEND:20150120T171500Z
UID:TALK56678@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Abstract: Rational points on Kummer varieties can be studied t
 hrough\nthe variation of Selmer groups of quadratic twists of the underlyi
 ng abelian variety\,\nusing an idea of Swinnerton-Dyer. We consider the ca
 se when the Galois\naction on 2-torsion has a large image. Under a mild ad
 ditional assumption\nwe prove the Hasse principle assuming the finiteness 
 of relevant Shafarevich-Tate groups.\nThis approach is inspired by the wor
 k of Mazur and Rubin.
LOCATION:MR13
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