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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

[1] Artin, E., Tate, J., Class Field Theory, Benjamin, 1967.Google Scholar
[2] Cassels, J. W. S., Fröhlich, A. (Eds.), Algebraic Number Theory, Academic Press, 1967.Google Scholar
[3] Fried, M. D., Jarden, M., Field Arithmetic, Springer 1986.CrossRefGoogle Scholar
[4] Iyanaga, S., The Theory of Numbers, North-Holland, 1975.Google Scholar
[5] Lang, S., Algebraic Number Theory, Addison-Wesley, 1970.Google Scholar
[6] Rosen, M., The Hilbert class field in function fields, Expo. Math., 5 (1987), 365–378.Google Scholar
[7] Rosen, M., S-units and S-class group in algebraic function fields, J. of Algebra, 26 (1973), 98–108.CrossRefGoogle Scholar
[8] Weil, A., Basic Number Theory, Springer, 1967.CrossRefGoogle Scholar
[9] Weiss, E., Algebraic Number Theory, McGraw-Hill, 1963.Google Scholar