Sequences of rational torsions on abelian varieties
type: Item
instance of: scholarly article
title: Sequences of rational torsions on abelian varieties
zbMATH Open document ID: 0788.14040
DOI: 10.1007/BF01243919
published in: Inventiones Mathematicae
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/143948
review text: The author gives some families of special curves of higher genus, which contain a rational torsion divisor whose order depends linearly or quadratically on the genus. Moreover, by using the jacobian varieties of these special curves, he notes that there exists a series of abelian varieties over \(\mathbb{Q}\) with a rapidly increasing sequence of torsions. For the elliptic curves over \(\mathbb{Q}\), \textit{B. Mazur} [in Modular Funct. one Variable, V. Proc. internat. Conf., Bonn 1976, Lect. Notes Math. 601, 107-148 (1977; Zbl 0357.14005)] decides the rational torsions on them.
reviewed by: Tsutomu Sekiguchi
Mathematics Subject Classification ID: 14K30
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14H40
zbMATH DE Number: 59807
zbMATH Keywords: families of curves of higher genus
zbMATH Keywords: jacobian varieties
zbMATH Keywords: rational torsions
author: E. Victor Flynn
MaRDI profile type: Publication
cites work: On the integration of algebraic functions
cites work: Large rational torsion on abelian varieties
cites work: Q3728129
cites work: Torsion points on elliptic curves over all quadratic fields
cites work: Q4129569
cites work: On the arithmetic of abelian varieties
cites work: Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields
cites work: On the fractional parts of {x/n} and related sequences. II, III
cites work: Q4732552
description: scientific article; zbMATH DE number 59807