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Parity of ranks of abelian surfaces

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  • UserCeline Maistret (University of Bristol)
  • ClockTuesday 24 October 2017, 14:30-15:30
  • HouseMR13.

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

Let K be a number field and A/K an abelian surface. By the Mordell-Weil theorem, the group of K-rational points on A is finitely generated and as for elliptic curves, its rank is predicted by the Birch and Swinnerton-Dyer conjecture. A basic consequence of this conjecture is the parity conjecture: the sign of the functional equation of the L-series determines 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 unconditional results for Selmer groups.

This talk is part of the Number Theory Seminar series.

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