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Explicit quadratic Chabauty over number fields

Balakrishnan, J. S., Besser, A., Bianchi, F. & Müller, J. S., 10-Oct-2019, In : ArXiv.

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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.
Original languageEnglish
JournalArXiv
Publication statusPublished - 10-Oct-2019

    Keywords

  • math.NT, Primary 11G30, Secondary 11S80, 11Y50, 14G40

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