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On Rationality of Algebraic Function Fields

Published online by Cambridge University Press:  20 November 2018

Nobuo Nobusawa
Nobuo Nobusawa*
Affiliation:
University of Hawaii, Honolulu
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Let A be an algebraic function field with a constant field k which is an algebraic number field. For each prime p of k, we consider a local completion kp and set Ap = Ak ꕕ kp. Then we have the question:

Is it true that A/k is a rational function field (i.e., A is a purely transcendental extension of k) if Ap/kp is so for every p ? In this note we shall discuss the question in a slightly different and hence easier case.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 3 , June 1969 , pp. 339 - 341
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Artin, E. and Tate, J., Class field theory. (Harvard, 1961).Google Scholar
2. Roquette, P., On the Galois cohomology of the projective linear group and its applications. Math. Ann. 150 (1963) 411–439.Google Scholar