## Title data

Stoll, Michael:

**Chabauty without the Mordell-Weil group.**

*In:* Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter
(ed.):
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. -
Cham
: Springer
,
2017
. - pp. 623-663

ISBN 978-3-319-70565-1

DOI: https://doi.org/10.1007/978-3-319-70566-8_28

## Project information

Project title: |
Project's official title Project's id Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory SPP 1489 |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

Based on ideas from recent joint work with Bjorn Poonen, we describe an algorithm that can in certain cases determine the set of rational points on a curve C, given only the p-Selmer group S of its Jacobian (or some other abelian variety C maps to) and the image of the p-Selmer set of C in S. The method is more likely to succeed when the genus is large, which is when it is usually rather difficult to obtain generators of a finite-index subgroup of the Mordell-Weil group, which one would need to apply Chabauty’s method in the usual way. We give some applications, for example to generalized Fermat equations of the form x^5 + y^5 = z^p.

## Further data

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

Refereed: | Yes |

Keywords: | Rational points on curves; Chabauty’s method; Selmer group |

Subject classification: | Mathematics Subject Classification Code: 11G30 14G05 14G25 14H25 11Y50 11D41 |

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: | 20 Jun 2018 11:29 |

Last Modified: | 20 Jun 2018 11:29 |

URI: | https://eref.uni-bayreuth.de/id/eprint/44579 |