Explicit quadratic Chabauty over number fields

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 clas...

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Bibliographic Details
Published in:Israel journal of mathematics 2021-06, Vol.243 (1), p.185-232
Main Authors: Balakrishnan, Jennifer S., Besser, Amnon, Bianchi, Francesca, Müller, J. Steffen
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Number theory
Scalars
Theoretical
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Summary: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-021-2158-5