Torsion points in families of Drinfeld modules

Dragos Ghioca ; Liang-Chung Hsia

Acta Arithmetica, Tome 161 (2013), p. 219-240 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2013-01-01

Zbl 1306.11048

EUDML-ID : urn:eudml:doc:279841