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arXiv · 1910.04653

Explicit quadratic Chabauty over number fields

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

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Jennifer S. Balakrishnan, Amnon Besser, Francesca Bianchi, J. Steffen Müller. 2019-10-10. Explicit quadratic Chabauty over number fields. https://arxiv.org/abs/1910.04653

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