On the parity conjecture for abelian surfaces

Celine Maistret; Vladimir Dokchitser

doi:10.1112/plms.12545

On the parity conjecture for abelian surfaces

Celine Maistret^*
, Vladimir Dokchitser

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	295-365
Number of pages	71
Journal	Proceedings of the London Mathematical Society
Volume	127
Issue number	2
Early online date	19 Jul 2023
DOIs	https://doi.org/10.1112/plms.12545
Publication status	Published - 2 Aug 2023

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Arithmetic of hyperelliptic curves.
Dokchitser, T. (Principal Investigator)
1/06/15 → 30/11/18
Project: Research

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title = "On the parity conjecture for abelian surfaces",

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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AB - 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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DO - 10.1112/plms.12545

M3 - Article (Academic Journal)

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SP - 295

EP - 365

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 2

ER -

On the parity conjecture for abelian surfaces

Abstract

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Projects

Arithmetic of hyperelliptic curves.

Cite this