Parity conjecture for abelian surfaces

2019/11/12 by Vladimir Dokchitser, Céline Maistret, Dokchitser, Vladimir +1 · 1 citation
Arts and Humanities · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.04626

openalex publication_date 2019/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Local constancy of reduction type and related invariants for curves in p-adic families

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