Torsion points in families of Drinfeld modules

• Autorzy: Dragos Ghioca , Liang-Chung Hsia
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37P05: Polynomial and rational maps
• 37P10: Analytic and meromorphic maps

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 3
• Strony: 219-240

Daty

wydano

2013

Twórcy

autor

Dragos Ghioca

• Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

autor

Liang-Chung Hsia

• Department of Mathematics, National Taiwan Normal University, Taiwan, ROC

Identyfikatory

DOI

10.4064/aa161-3-2