Abelian Varieties and Galois Extensions of Hilbertian Fields

TL;DR

This paper proves a conjecture by Moshe Jarden that certain intermediate fields of Galois extensions related to abelian varieties over Hilbertian fields are themselves Hilbertian, advancing understanding in field theory and algebraic geometry.

Contribution

It establishes the validity of the Kuykian conjecture for Galois extensions of Hilbertian fields, a significant step in the study of abelian varieties and field extensions.

Findings

The conjecture holds for Galois extensions of Hilbertian fields.

Intermediate fields of K(A_{tor})/K are Hilbertian in the Galois case.

Supports broader conjectures about field extensions and abelian varieties.

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}).