The Mathematical Institute, University of Oxford, Eprints Archive

A flexible method for applying Chabauty's Theorem

Flynn, E. V. (1997) A flexible method for applying Chabauty's Theorem. Compositio Mathematica, 105 . pp. 79-94. ISSN 0010-437X

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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 C(Q) for a selection of curves. A fringe benefit is a more explicit proof of a result of Coleman.

Item Type:Article
Uncontrolled Keywords:Chabauty's Theorem; hyperelliptic curves.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:265
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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