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A Generalization of Global Class Field Theory

Published online by Cambridge University Press:  20 November 2018

Tae Kun Seo  and
G. Whaples
Tae Kun Seo
Affiliation:
Indiana University, Bloomington, Indiana
G. Whaples
Affiliation:
University of Kentucky, Lexington, Kentucky University of Massachusetts, Boston, Massachusetts
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Let R be a field of rational functions of one variable over a field of constants R 0. Dock Sang Rim (6) has proved that the global reciprocity law in exactly the usual sense holds whenever R 0 is an absolutely algebraic quasi-fini te field of characteristic not equal to 0: this was known before only when R 0 was a finite field. We shall give another proof of Rim's result by means of a noteworthy generalization of the usual global reciprocity law. Namely, let R 0 be a finite field and let F be the set of all fields k contained in some fixed R alg.clos. and of finite degree over R. The reciprocity law states that there exists a family {fk }, k ∈ F, of functions fk : Ck → G(k abel.clos./k) (where Ck is the idèle class group of k) enjoying certain properties such as the norm transfer law.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 609 - 614
Copyright
Copyright © Canadian Mathematical Society 1969

References

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