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Global Norm-Residue Map over Quasi-Finite Field

Published online by Cambridge University Press:  22 January 2016

D. S. Rim  and
G. Whaples
D. S. Rim
Affiliation:
University of Pennsylvania, Indiana University, University of Notre Dame
G. Whaples
Affiliation:
University of Pennsylvania, Indiana University, University of Notre Dame
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A field k is called quasi-finite if it is perfect and if Gk≈Ż where Gk is the Galois group of the algebraic closure kc over k and Ż is the completion of the additive group of the rational integers. The classical reciprocity law on the local field with finite residue field is well-known to hold on local fields with quasi-finite residue field ([4] [5]). Thus it is natural to ask if the global reciprocity law should hold in the ordinary sense (see § 1 below) on the function-fields of one variable over quasi-finite field. We consider here two basic prototypes of non-finite quasi-finite fields:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 323 - 329
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Cartan, H. and Eilenberg, S., Homological Algebra.Google Scholar
[2] Lang, S. and Tate, J., Principal homogeneous spaces over abelian varieties, American Journal of Math., vol. 80 (1958), pp. 659–684.Google Scholar
[3] Serre, J. P., Cohomologie Galoisienne, College de France, 1963.Google Scholar
[4] Serre, J. P., Corps Locaux, Hermann, 1962.Google Scholar
[5] Whaples, G., Generalized local class field theory, I Duke Math. Journal, vol. 19 (1952), pp. 505–517.Google Scholar