Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves

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

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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 the rationals.
Original languageEnglish
JournalJournal fur die Reine und Angewandte Mathematik
StatePublished - 2013

Keywords

  • Mathematics - Number Theory
  • Mathematics - Algebraic Geometry
  • 11S80
  • 14G40
  • 11Y50 (Primary)
  • 11G30
  • 11D41 (Secondary)

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