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

Title data

Stoll, Michael:
On the arithmetic of the curves y² = xˡ + A and their Jacobians.
In: Journal für die Reine und Angewandte Mathematik. Vol. 501 (August 1998) . - pp. 171-189.
ISSN 0075-4102
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.

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
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - 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: 04 Feb 2015 09:28
URI: https://eref.uni-bayreuth.de/id/eprint/6234