Quadratic Chabauty: padic height pairings and integral points on hyperelliptic curves
Abstract
We give a formula for the component at p of the padic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabautylike method for finding padic approximations to pintegral points on such curves when the MordellWeil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such pintegral 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 MordellWeil group tensored with the rationals.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 arXiv:
 arXiv:1302.2944
 Bibcode:
 2013arXiv1302.2944B
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11S80;
 14G40;
 11Y50 (Primary);
 11G30;
 11D41 (Secondary)
 EPrint:
 27 pages