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Ramification Theory for Extensions of Degree p. II

Published online by Cambridge University Press:  22 January 2016

Susan Williamson
Susan Williamson*
Affiliation:
Regis College Weston, Massachusetts
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Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 46 , March 1972 , pp. 97 - 109
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Artin, E. and Tate, J., Class field theory, Benjamin, (1967).Google Scholar
[2] Cassels, J.W.S. and Frolich, A., Algebraic Number Theory, Thompson, (1967).Google Scholar
[3] Nagata, M., Local Rings, Wiley, (1962).Google Scholar
[4] Serre, J.-P., Corps Locaux, Paris, Hermann, (1962).Google Scholar
[5] Williamson, S., Ramification theory for extensions of degree p, Nagoya Math. J. Vol. 41 (1971), pp. 149–168.Google Scholar