## Title data

Cremona, John E. ; Fisher, Tom A. ; O'Neil, C. ; Simon, D. ; Stoll, Michael:

**Explicit n-descent on elliptic curves, II. Geometry.**

*In:* Journal für die Reine und Angewandte Mathematik.
(2009)
Issue 632
.
- pp. 63-84.

ISSN 1435-5345

DOI: https://doi.org/10.1515/CRELLE.2009.050

## Abstract in another language

This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly as curves of degree n embedded in P^(n-1). The main tool we use is a comparison between an easily obtained embedding into P^(n^2-1) and another map into P^(n^2-1) that

factors through the Segre embedding P^(n-1) x P^(n-1) -> P^(n^2 - 1). The comparison relies on an explicit version of the local-to-global principle for the n-torsion of the Brauer group of the base field.

## Further data

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

Refereed: | Yes |

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: | 26 Jan 2015 11:21 |

Last Modified: | 03 May 2022 12:40 |

URI: | https://eref.uni-bayreuth.de/id/eprint/6014 |