Dokchitser, Vladimir;
Maistret, Celine;
(2023)
On the parity conjecture for abelian surfaces.
Proceedings of the London Mathematical Society
10.1112/plms.12545.
(In press).
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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.
| Type: | Article |
|---|---|
| Title: | On the parity conjecture for abelian surfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/plms.12545 |
| Publisher version: | https://doi.org/10.1112/plms.12545 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10174300 |
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