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

Details The Mordell-Weil sieve: Proving non-existence of rational points on curves The Mordell-Weil sieve: Proving non-existence of rational points on curves

2009-06-10

arxiv.org/abs/0906.1934v2

Mathematics

Number Theory

47 pages, 4 figures. Revised version, following suggestions/questions by the referee. Main changes: (1) We fixed a gap in the

Scientific paper

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.

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