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SUMMARY:Parity of ranks of abelian surfaces - Celine Maistret (University 
 of Bristol)
DTSTART:20171024T133000Z
DTEND:20171024T143000Z
UID:TALK84211@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Let K be a number field and A/K an abelian surface. By the Mor
 dell-Weil theorem\, the group of K-rational points on A is finitely genera
 ted and as for elliptic curves\, its rank is predicted by the  Birch and S
 winnerton-Dyer conjecture. A basic consequence of this conjecture is the p
 arity conjecture: the sign of the functional equation of the L-series dete
 rmines the parity of the rank of A/K. Under suitable local constraints and
  finiteness of the Shafarevich-Tate group\, we prove the parity conjecture
  for principally polarized abelian surfaces. We also prove analogous uncon
 ditional results for Selmer groups.
LOCATION:MR13
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