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A Theorem of Harrison, Kummer Theory, and Galois Algebras

Published online by Cambridge University Press:  22 January 2016

S. U. Chase  and
Alex Rosenberg
S. U. Chase
Affiliation:
Cornell University, Ithaca, New York, U.S.A.
Alex Rosenberg
Affiliation:
Cornell University, Ithaca, New York, U.S.A.
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Let R be a field and S a separable algebraic closure of R with galois group R. In [8] Harrison succeeded in describing R/′R in terms of R only. More precisely, he constructed a certain complex (R, Q/Z) and proved Homc, where Homc denotes continuous homomorphisms and H2 stands for the second cohomology group of the complex . In this paper, which is mainly expository in nature, we reexamine Harrison’s proof and show how [8] connects with Kummer theory and the theory of galois algebras [16]. We emphasize that most of the ideas on which this paper is based originate in [8].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 663 - 685
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

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