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On the Existence of Unramified Separable Infinite Solvable Extensions of Function Fields over Finite Fields*

Published online by Cambridge University Press:  22 January 2016

Hisasi Morikawa
Hisasi Morikawa*
Affiliation:
Mathematical Institute, Nagoya University
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In the present note, using the results in the previous paper, we shall prove the following existence theorem:

THEOREM. Let k be a finite field with q elements and K/k be a regular extension of dimension one over k. Then, if q ≧ 11 and the genus gK of K/k is greater than one, there exists an unramified separable infinite solvable extension of K ivhich is regular over k.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 13 , June 1958 , pp. 95 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1958

Footnotes

*

This note was prepared while the author was a Yukawa Fellow at Osaka University.

References

[1] Morikawa, H., Generalized jacobian varieties and separable abelian extension of function fields, Nagoya Journal, 12 (1957), pp. 231–254.Google Scholar