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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Brauer-Hilbertian fields

Authors: Burton Fein, David J. Saltman and Murray Schacher
Journal: Trans. Amer. Math. Soc. 334 (1992), 915-928
MSC: Primary 12E25; Secondary 12G05, 13A20
MathSciNet review: 1075382
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Abstract: Let $ F$ be a field of characteristic $ p$ ($ p = 0$ allowed), and let $ F(t)$ be the rational function field in one variable over $ F$. We say $ F$ is Brauer-Hilbertian if the following holds. For every $ \alpha $ in the Brauer group $ \operatorname{Br}(F(t))$ of exponent prime to $ p$, there are infinitely many specializations $ t \to a \in F$ such that the specialization $ \bar \alpha \in \operatorname{Br}(F)$ is defined and has exponent equal to that of $ \alpha $. We show every global field is Brauer-Hilbertian, and if $ K$ is Hilbertian and $ F$ is finite separable over $ K(t)$, $ F$ is Brauer-Hilbertian.

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PII: S 0002-9947(1992)1075382-0
Keywords: Brauer group, Brauer-Hilbertian, corestriction, Hilbertian
Article copyright: © Copyright 1992 American Mathematical Society