Abelian Varieties and Galois Extensions of Hilbertian Fields

2011/03/11 by Thornhill, Christopher · 1 citation
#14kxx (12E25 12E30) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1103.2333

Abstract

In a recent paper, Moshe Jarden proposed a conjecture, later named the Kuykian conjecture, which states that if A is an abelian variety defined over a Hilbertian field K, then every intermediate field of K(A_tor)/K is Hilbertian. We prove that the conjecture holds for Galois extensions of K in K(A_tor).

Cited by

• Hilbert properties of varieties

Related

• Hilbertian fields and Galois representations
• Absolutely Abelian Hilbert Class Fields and ℓ-torsion conjecture
• Fully Hilbertian Fields
• Hilbertian fields and Hilbert's irreducibility theorem
• Hilbert irreducibility for abelian varieties over function fields of characteristic zero