Explicit quadratic Chabauty over number fields

Jennifer S. Balakrishnan, Amnon Besser, Francesca Bianchi, J. Steffen Müller

Published 2019-10-10Version 1

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.