Torsion points in families of Drinfeld modules

Dragos Ghioca, and Liang-Chung Hsia. "Torsion points in families of Drinfeld modules." Acta Arithmetica 161.3 (2013): 219-240. <http://eudml.org/doc/279841>.

@article{DragosGhioca2013,
abstract = {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.},
author = {Dragos Ghioca, Liang-Chung Hsia},
journal = {Acta Arithmetica},
keywords = {Drinfeld modules; torsion points; Manin-Mumford conjecture},
language = {eng},
number = {3},
pages = {219-240},
title = {Torsion points in families of Drinfeld modules},
url = {http://eudml.org/doc/279841},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Dragos Ghioca
AU - Liang-Chung Hsia
TI - Torsion points in families of Drinfeld modules
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 3
SP - 219
EP - 240
AB - 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.
LA - eng
KW - Drinfeld modules; torsion points; Manin-Mumford conjecture
UR - http://eudml.org/doc/279841
ER -