On torsion sections of elliptic fibrations

2005/09/07 by Siman Wong, Wong, Siman
Mathematics · #11G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G35

paper · pdf · doi:10.48550/arxiv.math/0509168

arxiv created 2005/09/07 · arxiv updated 2009/12/01

Abstract

Let E be an elliptic curve over the function field Q(t). Suppose that for every number field L\not=Q and every element tau∈ L such that the specialization E_tau is smooth, the curve E_tau has a non-trivial torsion point over L. We show that E has a non-trivial torsion point over Q(t). This provides evidence in support of a question of Graber-Harris-Mazur-Starr on rational pseudo-sections of arithmetic surjective morphisms.

Related

• On the torsion values for sections of an elliptic scheme
• Pursuing polynomial bounds on torsion
• Typically bounding torsion on elliptic curves with rational\n j-invariant
• Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of ℚ
• Torsion of Rational Elliptic Curves over the ℤ_p-Extensions of Quadratic Fields