Torsion points in families of Drinfeld modules

2012/06/29 by Ghioca, Dragos, Hsia, Liang-Chung
#11S82 #37P05 #37P10 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1206.7047

Abstract

Let Φ^ł be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let \bfa,\bfb∈ K[ł]. Assume that neither \bfa(ł) nor \bfb(ł) is a torsion point for Φ^ł for all ł. If there exist infinitely many ł∈\Kbar such that both \bfa(ł) and \bfb(ł) are torsion points for Φ^ł, then we show that for each ł∈\Kbar, we have that \bfa(ł) is torsion for Φ^ł if and only if \bfb(ł) is torsion for Φ^ł. In the case \bfa,\bfb∈ K, then we prove in addition that \bfa and \bfb must be \Fpbar-linearly dependent.

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