## Brauer-Hilbertian fields

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- by Burton Fein, David J. Saltman and Murray Schacher PDF
- Trans. Amer. Math. Soc.
**334**(1992), 915-928 Request permission

## 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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## Additional Information

- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**334**(1992), 915-928 - MSC: Primary 12E25; Secondary 12G05, 13A20
- DOI: https://doi.org/10.1090/S0002-9947-1992-1075382-0
- MathSciNet review: 1075382