Explicit quadratic Chabauty over number fields

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

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)185–232
JournalIsrael journal of mathematics
Volume243
Early online date8-Jun-2021
DOIs
Publication statusPublished - Jun-2021

Keywords

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

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