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SUMMARY:Parity of Selmer ranks in quadratic twist families - Adam Morgan (
 KCL)
DTSTART:20161011T133000Z
DTEND:20161011T143000Z
UID:TALK67451@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:The Shafarevich--Tate group of an elliptic curve over a number
  field has square order (if finite) as a consequence of the Cassels--Tate 
 pairing. For general principally polarised abelian varieties\, however\, t
 his can fail to be the case. We examine how this phenomenon behaves under 
 quadratic twist and derive consequences for the behaviour of 2-Selmer rank
 s in quadratic twist families. Specifically\, we prove results about the p
 roportion of twists of a fixed principally polarised abelian variety havin
 g odd (resp. even) 2-Selmer rank\, generalising work of Klagsbrun–Mazur
 –Rubin for elliptic curves and Yu for Jacobians of hyperelliptic curves.
  We exhibit several new features of the statistics which were not present 
 in these settings. 
LOCATION:MR13
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