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

 

Alternating forms and the Brauer group of a geometric field


Author: Eric S. Brussel
Journal: Trans. Amer. Math. Soc. 359 (2007), 3025-3069
MSC (2000): Primary 16K50; Secondary 20J06
Published electronically: January 29, 2007
MathSciNet review: 2299445
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Abstract: We compute the theory of $ H^{2}(G,\mathbb{Q}/\mathbb{Z})$ for any proabelian group $ G$, using a natural isomorphism with the group $ \operatorname{Alt}(G,\mathbb{Q}/\mathbb{Z})$ of continuous alternating forms. We use this to establish a sort of generic behavioral ideal, or role model, for the Brauer group Br$ (F)$ of a geometric field $ F$ of characteristic zero. We show this ideal is attained in several interesting cases.


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Additional Information

Eric S. Brussel
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: brussel@mathcs.emory.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-03988-8
PII: S 0002-9947(07)03988-8
Received by editor(s): September 16, 2003
Received by editor(s) in revised form: March 7, 2005
Published electronically: January 29, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.