Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 12E25, 12G05, 13A20

Retrieve articles in all journals with MSC: 12E25, 12G05, 13A20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1075382-0
PII: S 0002-9947(1992)1075382-0
Keywords: Brauer group, Brauer-Hilbertian, corestriction, Hilbertian
Article copyright: © Copyright 1992 American Mathematical Society