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genus theory for function fields

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  09 April 2009

Sunghan Bae  and
Ja Kyung Koo
Sunghan Bae
Affiliation:
Department of MathematicsKorea Advanced Institute of Science and TechnologyTaejon, 305–701, Korea
Ja Kyung Koo
Affiliation:
Department of MathematicsKorea Advanced Institute of Science and TechnologyTaejon, 305–701, Korea
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Abstract

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We study the genus theory for function fields which is the analogue of the classical genus theory developed by Hasse and Fröhlich.

MSC classification

Secondary: 11R58: Arithmetic theory of algebraic function fields 11R29: Class numbers, class groups, discriminants
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 3 , June 1996 , pp. 301 - 310
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Clement, R., ‘The genus field of an algebraic function field’, J. Number Theory 40 (1992), 359–375.Google Scholar
[2]Fröhlich, A., Central extensions, Galois groups, and ideal class groups of number fields, Contemp. Math. 24 (Amer. Math. Soc., Providence, 1983).CrossRefGoogle Scholar
[3]Hasse, H., ‘Zur Geschlecht Theorie in quadratischen Zahlkörpern’, J. Math. Soc. Japan 3 (1951), 45–51.CrossRefGoogle Scholar
[4]Hayes, D., ‘Explicit class field theory for rational function fields’, Trans. Amer. Math. Soc. 189 (1974), 77–91.Google Scholar
[5]Hayes, D., ‘Stickelberger elements in function fields’, Compositio Math. 55 (1985), 209–239.Google Scholar
[6]Rosen, M., ‘The Hilbert class field in function fields’, Exposition. Math. 5 (1987), 365–378.Google Scholar