## 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 (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - 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 |