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A note on ray class fields of global fields

Published online by Cambridge University Press:  22 January 2016

Franz Halter-Koch
Franz Halter-Koch*
Affiliation:
Institut für Mathematik, Karl-Franzens- Universität, Halbärthgasse 1/I, A-8010 Graz, Österreich
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The notion of a ray class field, which is fundamental in Takagi’s class field theory, has no immediate analogon in the function field case. The reason for this lies in the lacking of a distinguished maximal order. In this paper I overcome this difficulty by a relative version of the notion of ray class fields to be defined for every holomorphy ring of the field. The prototype for this new notion is M. Rosen’s definition of a Hilbert class field for function fields [6].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 120 , December 1990 , pp. 61 - 66
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

Literature

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