Explicit quadratic Chabauty over number fields
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First author draft
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DOI
Authors
Balakrishnan, Jennifer
Besser, Amnon
Bianchi, Francesca
Mueller, J. Steffen
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First author draft
Citation
Jennifer Balakrishnan, Amnon Besser, Francesca Bianchi, J Steffen Mueller. "Explicit quadratic Chabauty over number fields." Israel Journal of Mathematics. https://arxiv.org/pdf/1910.04653.pdf.
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 Siksekās 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.