Parity conjecture for abelian surfaces

Vladimir Dokchitser; Celine Maistret

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arXiv · 1911.04626

Parity conjecture for abelian surfaces

Vladimir Dokchitser·Celine Maistret

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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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Vladimir Dokchitser, Celine Maistret. 2019-11-12. Parity conjecture for abelian surfaces. https://arxiv.org/abs/1911.04626

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