Almost locally free fields
type: Item
instance of: scholarly article
title: Almost locally free fields
zbMATH Open document ID: 1279.14036
author: Moshe Jarden
published in: Journal of Algebra
publication date: 2012-01-04T00:00:00Z
review text: A profinite group \(G\) is called \textit{almost \(\omega\)-free}, if every finite embedding problem \((G\twoheadrightarrow A\twoheadleftarrow B|\) \(A,B\) : finite\()\) has a virtual solution from an open subgroup of \(G\) onto \(B\). A profinite group \(G\) is called \textit{almost locally free}, if for each positive integer \(e\) and for almost all \(e\)-tuple \((\sigma_1,\dots,\sigma_e)\in G^e\) in the sense of the Haar measure, the closed subgroup generated by \(\sigma_1,\dots,\sigma_e\) is free on \(e\)-generators. It is shown that an almost locally free profinite group is almost \(\omega\)-free. Using the generalized Abhyankar's conjecture, the author deduces that the fundamental group of the smooth connected affine curve \(C\) over an algebraically closed field of positive characteristic is almost locally free, hence is almost \(\omega\)-free.
reviewed by: Hiroaki Nakamura
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 12E30
Mathematics Subject Classification ID: 14G17
Mathematics Subject Classification ID: 20E18
zbMATH DE Number: 5994284
zbMATH Keywords: Galois group
zbMATH Keywords: Abhyankar's conjecture
zbMATH Keywords: \(\omega \)-free groups
zbMATH Keywords: embedding problems
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.03.021
OpenAlex ID: W2009809682
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DOI: 10.1016/J.JALGEBRA.2011.03.021
description: scientific article; zbMATH DE number 5994284