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Two-cover descent on hyperelliptic curves

Title data

Bruin, Nils ; Stoll, Michael:
Two-cover descent on hyperelliptic curves.
In: Mathematics of Computation. Vol. 78 (October 2009) Issue 268 . - pp. 2347-2370.
ISSN 0025-5718
DOI: https://doi.org/10.1090/S0025-5718-09-02255-8

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Local-global obstruction; rational points; hyperelliptic curves; descent
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 21 Jan 2015 14:34
Last Modified: 27 Jan 2015 13:01
URI: https://eref.uni-bayreuth.de/id/eprint/5778