Explicit quadratic Chabauty over number fields
Number Theory
2020-06-16 v2
Abstract
We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary number fields using restriction of scalars. This is achieved by combining equations coming from Siksek's extension of classical Chabauty with equations defined in terms of p-adic heights attached to independent continuous idele class characters. We give several examples to show the practicality of our methods.
Cite
@article{arxiv.1910.04653,
title = {Explicit quadratic Chabauty over number fields},
author = {Jennifer S. Balakrishnan and Amnon Besser and Francesca Bianchi and J. Steffen Müller},
journal= {arXiv preprint arXiv:1910.04653},
year = {2020}
}
Comments
Fixed minor issues following the referee's suggestions; 33 pages