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Parity conjecture for abelian surfaces
Published 12 Nov 2019 in math.NT | (1911.04626v4)
Abstract: Assuming finiteness of the Tate--Shafarevich group, we prove that the Birch--Swinnerton-Dyer conjecture correctly predicts the parity of the rank of semistable principally polarised abelian surfaces. If the surface in question is the Jacobian of a curve, we require that the curve has good ordinary reduction at 2-adic places.
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