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Generalized Jacobian Varieties and Separable Abelian Extensions of Function Fields

Published online by Cambridge University Press:  22 January 2016

Hisasi Morikawa
Hisasi Morikawa*
Affiliation:
Mathematical Institute, Nagoya University
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Using Frobenius automorphisms ingeniouslly, S. Lang has established an elegant theory of unramified class fields of function fields in several variables over finite fields [2]. As an application of class field theory and theory of reduction he has proved that any separable unramified abelian extension of a function field of one variable comes from a pull back of a separable ingeny of its jacobian variety [3].

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 231 - 254
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Igusa, J., Fibre systems of Jocobian varieties I, Amer. Jour, of Math., vol. 78, No. 2.Google Scholar
[2] Lang, S., Unramified class field theory over function fields in several variables, Ann. of Math., vol. 64 (1954).Google Scholar
[3] Lang, S., On the Lefschetz principle, Ann. of Math., vol. 64 (1956).CrossRefGoogle Scholar
[4] Rosenlicht, M., Equivalence relation on algebraic curves, Ann. of Math., 56 (1952).Google Scholar
[5] Rosenlicht, M., Generalized jacobian varieties, Ann. of Math., vol. 59 (1954).Google Scholar
[6] Weil, A., The field of definition of a variety, Amer. Jour, of Math., vol. 78, No. 3.Google Scholar