The regular inverse Galois problem over non-large fields
type: Item
instance of: scholarly article
title: The regular inverse Galois problem over non-large fields
zbMATH Open document ID: 1159.12310
DOI: 10.4171/JEMS/15
author: Jochen Koenigsmann
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2005-02-28T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: By a celebrated theorem of Harbater and Pop, the regular inverse Galois problem is solvable over any field containing a large field. Using this and the Mordell conjecture for function fields, we construct the first example of a field \(K\) over which the regular inverse Galois problem can be shown to be solvable, but such that \(K\) does not contain a large field. The paper is complemented by model-theoretic observations on the diophantine nature of the regular inverse Galois problem.
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 03C68
zbMATH DE Number: 2139678
zbMATH Keywords: regular inverse Galois problem
zbMATH Keywords: embedding problems
zbMATH Keywords: large fields: Mordell conjecture for function fields
zbMATH Keywords: diophantine theory of fields
MaRDI profile type: Publication
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OpenAlex ID: W2067499760
description: scientific article; zbMATH DE number 2139678