## Title data

Stoll, Michael:

**On the arithmetic of the curves y² = xˡ + A and their Jacobians.**

*In:* Journal für die Reine und Angewandte Mathematik.
(1998)
Issue 501
.
- pp. 171-189.

ISSN 1435-5345

DOI: https://doi.org/10.1515/crll.1998.076

## Project information

Project financing: |
Deutsche Forschungsgemeinschaft The author thanks the Deutsche Forschungsgemeinschaft for supporting the present work by a research grant and the University of Oxford's Mathematical Institute for the hospitality during a two months' stay in 1996. |
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## Abstract in another language

Let l be an odd prime, and for a non-zero integer A, let C_A be the normalization of the curve given by the affine equation y^2 = x^l + A, and let J_A be its Jacobian, which is a 1/2(l-1)-dimensional abelian variety defined over Q. We use a method invented by Ed Schaefer to compute the (1-zeta_l)-Selmer grou Sel^(1-zeta_l)(K,J_A) of J_A over K=Q(zeta_l) under suitable hypotheses on A. This leads to bouds for the Mordell-Weil ranks of J_A(K) and of J_A(Q).

## Further data

Item Type: | Article in a journal |
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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: | No |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 03 Feb 2015 10:42 |

Last Modified: | 03 May 2022 12:36 |

URI: | https://eref.uni-bayreuth.de/id/eprint/6234 |