Quadratic chabauty: P-adic heights and integral points on hyperelliptic curves

Jennifer S. Balakrishnan, Amnon Besser, J. Steffen Müller

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use the method in explicit computation. An important aspect of the method is that it only requires a basis of the Mordell-Weil group tensored with Q.

Original languageEnglish
Pages (from-to)51-79
Number of pages29
JournalJournal fur die Reine und Angewandte Mathematik
Volume2016
Issue number720
DOIs
StatePublished - 1 Nov 2016

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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