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A flexible method for applying Chabauty's Theorem

Published online by Cambridge University Press:  04 December 2007

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

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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.

Keywords

Jacobianscurvesrational PointsChabautyformal groups
Type
Research Article
Information
Compositio Mathematica , Volume 105 , Issue 1 , January 1997 , pp. 79 - 94
Copyright
© 1997 Kluwer Academic Publishers