## Title data

Stoll, Michael:

**Independence of rational points on twists of a given curve.**

*In:* Compositio Mathematica.
Vol. 142
(2006)
Issue 5
.
- pp. 1201-1214.

ISSN 1570-5846

DOI: https://doi.org/10.1112/S0010437X06002168

## Abstract in another language

In this paper, we study bounds for the number of rational points on twists C' of a fixed curve C over a number field K, under the condition that the group of K-rational points on the Jacobian J' of C' has rank smaller than the genus of C'. The main result is that with some explicitly given finitely many possible exceptions, we have a bound of the form 2r+c, where r is the rank of J'(K) and c is a constant depending on C. For the proof, we use a refinement of the method of Chabauty-Coleman: the main new ingredient is to use it for an extension field of K_v, where v is a place of bad reduction for C'.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | rational points on curves; twists; Chabauty-Coleman method |

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: | No |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 03 Feb 2015 07:03 |

Last Modified: | 26 Sep 2023 10:49 |

URI: | https://eref.uni-bayreuth.de/id/eprint/6221 |