Parity conjecture for abelian surfaces
Number Theory
2023-05-16 v4
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.
Cite
@article{arxiv.1911.04626,
title = {Parity conjecture for abelian surfaces},
author = {Vladimir Dokchitser and Celine Maistret},
journal= {arXiv preprint arXiv:1911.04626},
year = {2023}
}
Comments
Appendix A by A. Morgan and Appendix B by T. Dokchitser and V. Dokchitser. Minor changes