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Torsion des courbes elliptiques sur les corps cubiques

Pierre Parent (2000)

Annales de l'institut Fourier

On donne la liste (à un élément près) des nombres premiers qui sont l’ordre d’un point de torsion d’une courbe elliptique sur un corps de nombres de degré trois.

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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