Dokchitser, T;
Dokchitser, V;
Maistret, C;
Morgan, A;
(2022)
Arithmetic of hyperelliptic curves over local fields.
Mathematische Annalen
10.1007/s00208-021-02319-y.
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Abstract
We study hyperelliptic curves y2= f(x) over local fields of odd residue characteristic. We introduce the notion of a “cluster picture” associated to the curve, that describes the p-adic distances between the roots of f(x), and show that this elementary combinatorial object encodes the curve’s Galois representation, conductor, whether the curve is semistable, and if so, the special fibre of its minimal regular model, the discriminant of its minimal Weierstrass equation and other invariants.
| Type: | Article |
|---|---|
| Title: | Arithmetic of hyperelliptic curves over local fields |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00208-021-02319-y |
| Publisher version: | https://doi.org/10.1007/s00208-021-02319-y |
| 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/ |
| Keywords: | 11G20, 11G10, 14D10, 14F20, 14H45 |
| UCL classification: | 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 UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10144539 |
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