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49
result(s) for
"Haran, Dan"
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Θ-Hilbertianity and strong Θ-Hilbertianity
Θ-Hilbertianity and its strengthening, strong Θ-Hilbertianity, are two generalizations of Hilbertianity inspired by Jarden’s definition of
p
-Hilbertianity and strong
p
-Hilbertianity. Jarden has asked whether the two notions defined by him are actually the same. We address this question in its more general version of Θ-Hilbertianity and show that for PRC, and, in particular, for PAC fields,
p
-Hilbertianity and strong
p
-Hilbertianity coincide.
Journal Article
Relatively projective pro-p groups
It is known that the Kurosh Subgroup Theorem does not hold for pro-
p
groups of large cardinality. However, a closed subgroup of a free pro-
p
product is projective relative to the Kurosh family of subgroups. In this paper we prove the converse of this fact.
Journal Article
Projective group structures as absolute Galois structures with block approximation
The authors prove: A proper profinite group structure $\\mathbf{G $ is projective if and only if $\\mathbf{G $ is the absolute Galois group structure of a proper field-valuation structure with block approximation.
eBook
On the uniqueness of the smallest embedding cover
Using group theoretic methods only, we prove the uniqueness of the smallest embedding cover of a profinite group, Problem 36.2.25 of Field Arithmetic, 4th edition.
Paper
Fundaments of epimorphisms of profinite groups
We propose and develop a theory that allows to characterize epimorphisms of profinite groups in terms of indecomposable epimorphisms.
Paper
Permanence criteria for semi-free profinite groups
We introduce the condition of a profinite group being semi-free, which is more general than being free and more restrictive than being quasi-free. In particular, every projective semi-free profinite group is free. We prove that the usual permanence properties of free groups carry over to semi-free groups. Using this, we conclude that if
k
is a separably closed field, then many field extensions of
k
((
x
,
y
)) have free absolute Galois groups.
Journal Article
