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arXiv · 1302.2944

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.

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Jennifer S. Balakrishnan, Amnon Besser, J. Steffen Müller. 2013-02-12. Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves. https://arxiv.org/abs/1302.2944

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