Green, Holly;
(2023)
The Parity Conjecture for Hyperelliptic Curves.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
The Birch and Swinnerton-Dyer conjecture famously predicts that the rank of an elliptic curve, or more generally an abelian variety, can be computed from its L- function. A consequence of this, known as the parity conjecture, is a purely arithmetic result which bypasses the conjectural theory of L-functions and asserts that the parity of the rank is determined by the root number. This thesis investigates the parity conjecture for Jacobians of hyperelliptic curves and collates some of the first pieces of evidence (beyond elliptic curves) for the Birch and Swinnerton-Dyer conjecture. In doing this, we exhibit formulae for the parity of the rank of certain abelian varieties which use only the local theory of curves.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | The Parity Conjecture for Hyperelliptic Curves |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2023. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| 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/10182441 |
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