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Torsion points in families of Drinfeld modules

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Ghioca D., Hsia L.-C.

Acta Arithmetica

2013

tom 161

nr 3

219-240

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 $𝔽̅_{p}$-linearly dependent.

Ograniczanie wyników

1 Acta Arithmetica

1 Ghioca D.

1 Hsia L.-C.

1 2013

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Torsion points in families of Drinfeld modules