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

Titelangaben

Balakrishnan, Jennifer S. ; Besser, Amnon ; Müller, Jan Steffen:
Quadratic Chabauty : p-adic heights and integral points on hyperelliptic curves.
In: Journal für die Reine und Angewandte Mathematik. (2016) Heft 720 . - S. 51-79.
ISSN 1435-5345
DOI: https://doi.org/10.1515/crelle-2014-0048

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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 ℚ.