Two-cover descent on hyperelliptic curves
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Publication:3055202
DOI10.1090/S0025-5718-09-02255-8zbMATH Open1208.11078arXiv0803.2052MaRDI QIDQ3055202
Author name not available (Why is that?)
Publication date: 7 November 2010
Published in: (Search for Journal in Brave)
Abstract: We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In particular, if the algorithm returns an empty set, then the hyperelliptic curve has no rational points. This provides a relatively efficiently tested criterion for solvability of hyperelliptic curves. We also discuss applications of this algorithm to curves of genus 1 and to curves with rational points.
Full work available at URL: https://arxiv.org/abs/0803.2052
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