PAC fields over number fields
Moshe Jarden (2006)
Journal de Théorie des Nombres de Bordeaux
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We prove that if is a number field and is a Galois extension of which is not algebraically closed, then is not PAC over .
Displaying similar documents to “Galois Covers and the Hilbert-Grunwald Property”
PAC fields over number fields
Non-existence and splitting theorems for normal integral bases
Cornelius Greither, Henri Johnston (2012)
Annales de l’institut Fourier
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We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower forces the tower to be split in a very strong sense.
On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.
Chipchakov, Ivan D. (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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Automatic realizations of Galois groups with cyclic quotient of order
Ján Mináč, Andrew Schultz, John Swallow (2008)
Journal de Théorie des Nombres de Bordeaux
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We establish automatic realizations of Galois groups among groups , where is a cyclic group of order for a prime and is a quotient of the group ring .
Hopf Galois structures on Kummer extensions of prime power degree.
Childs, Lindsay N. (2011)
The New York Journal of Mathematics [electronic only]
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On a general difference Galois theory I
Shuji Morikawa (2009)
Annales de l’institut Fourier
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We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic , we attach its Galois group, which is a group of coordinate transformation.