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The Mordell–Weil sieve: proving non-existence of rational points on curves

Published online by Cambridge University Press:  01 August 2010

Nils Bruin
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada (email: nbruin@cecm.sfu.ca)
Michael Stoll
Affiliation:
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany (email: Michael.Stoll@uni-bayreuth.de)

Abstract

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We discuss the Mordell–Weil sieve as a general technique for proving results concerning rational points on a given curve. In the special case of curves of genus 2, we describe quite explicitly how the relevant local information can be obtained if one does not want to restrict to mod p information at primes of good reduction. We describe our implementation of the Mordell–Weil sieve algorithm and discuss its efficiency.

Supplementary materials are available with this article.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2010

References

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