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Torsion points in families of Drinfeld modules

Dragos Ghioca, Liang-Chung Hsia (2013)

Acta Arithmetica

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

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