Torsion points in families of Drinfeld modules
Number Theory
2012-07-02 v1 Dynamical Systems
Abstract
Let be an algebraic family of Drinfeld modules defined over a field of characteristic , and let . Assume that neither nor is a torsion point for for all . If there exist infinitely many such that both and are torsion points for , then we show that for each , we have that is torsion for if and only if is torsion for . In the case , then we prove in addition that and must be -linearly dependent.
Keywords
Cite
@article{arxiv.1206.7047,
title = {Torsion points in families of Drinfeld modules},
author = {Dragos Ghioca and Liang-Chung Hsia},
journal= {arXiv preprint arXiv:1206.7047},
year = {2012}
}
Comments
17 pages. arXiv admin note: text overlap with arXiv:1102.2769