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

DOI10.1112/S1461157009000187zbMATH Open1278.11069arXiv0906.1934OpenAlexW3105065612MaRDI QIDQ3092002

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Publication date: 15 September 2011

Published in: (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/0906.1934

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