The Mathematical Institute, University of Oxford, Eprints Archive

Sequences of rational torsions on abelian varieties

Flynn, E. V. (1991) Sequences of rational torsions on abelian varieties. Inventiones Mathematicae, 106 . pp. 433-442. ISSN 0020-9910

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Abstract

We address the question of how fast the available rational torsion on abelian varieties over Q increases with dimension. The emphasis will be on the derivation of sequences of torsion divisors on hyperelliptic curves. Work of Hellegouarch and Lozach (and Klein) may be made explicit to provide sequences of curves with rational torsion divisors of orders increasing linearly with respect to genus. The main results are applications of a new technique which provide sequences of hyperelliptic curves for all torsions in an interval $[a_g, a_g+b_g]$ where $a_g$ is quadratic in g and $b_g$ is linear in g. As well as providing an improvement from linear to quadratic, these results provide a wide selection of torsion orders for potential use by those involved in computer integration. We conclude by considering possible techniques for divisors of non-hyperelliptic curves, and for general abelian varieties.

Item Type:Article
Uncontrolled Keywords:Torsion growth, abelian varieties, hyperelliptic curves.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:272
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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