Fully Hilbertian Fields

2009/07/02 by Bary-Soroker, Lior, Paran, Elad · 1 citation
#12E25 #12E30 #12F10 #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0907.0343

Abstract

We introduce the notion of fully Hilbertian fields, a strictly stronger notion than that of Hilbertian fields. We show that this class of fields exhibits the same good behavior as Hilbertian fields, but for fields of uncountable cardinality, is more natural than the notion of Hilbertian fields. In particular, we show it can be used to achieve stronger Galois theoretic results. Our proofs also provide a step toward the so-called Jarden-Lubotzky twinning principle.

Cited by

• Hilbert properties of varieties

Related

• Hilbertian fields and Hilbert's irreducibility theorem
• Hilbertian fields and Galois representations
• Abelian Varieties and Galois Extensions of Hilbertian Fields
• Θ-Hilbertianity and strong Θ-Hilbertianity
• Random Galois extensions of Hilbertian fields