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Note on Galois Cohomology
Published online by Cambridge University Press: 22 January 2016
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Let K/k be a Galois extension. Formerly the writer studied, in [3], [4], a certain correlation of factor sets in K/k with the norm class group of K/k, and extended it, in [5.], to 3-dimensional cocycles. The present note is to study the same relationship for general n-cocycles. As a matter of fact, the constructions which underlie the relationship have become common places in cohomology theory, through the works of French and American authors, and indeed the construction to bring certain (non-Galois) cocycles into the ground field k has been discussed by Baer [1, Theorem C] for general dimensions n under the setting of general group cohomology.
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- Research Article
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1953
References
[1]
Baer, R. : The cohomology theory of a pair of groups, Proc. Internat Congress of Mathematicians, 1950, Vol. II, p. 15.Google Scholar
[2]
Hochschild, G.- Nakayama, T.: Cohomology in class field theory, Ann. Math. 55 (1952), p. 348.Google Scholar
[3]
Nakayama, T. : Über die Beziehung zwischen den Faktorensystemen und der Normklassengruppe eines galoisschen Erweiterungskoerpers, Math. Ann.
112 (1935), p. 85.Google Scholar
[4]
Nakayama, T. : A theorem on the norm group of a finite extension field, Jap, J. Math.
18 (1943) p. 877.Google Scholar
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