Compositio Mathematica



A flexible method for applying Chabauty's Theorem


E. V. FLYNN a1
a1 Department of Pure Mathematics, University of Liverpool, P.O. Box 147, Liverpool, L69 3BX, England. e-mail: evflynn@liv.ac.uk

Article author query
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Abstract

A strategy is proposed for applying Chabauty's Theorem to hyperelliptic curves of genus ${>} 1$. In the genus 2 case, it shown how recent developments on the formal group of the Jacobian can be used to give a flexible and computationally viable method for applying this strategy. The details are described for a general curve of genus 2, and are then applied to find ${\bm C}({\bb Q})$ for a selection of curves. A fringe benefit is a more explicit proof of a result of Coleman.


Key Words: Jacobians; curves; rational Points; Chabauty; formal groups.