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Transactions of the American Mathematical Society

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Mayer-Vietoris sequences and Brauer groups of nonnormal domains

Author: L. N. Childs
Journal: Trans. Amer. Math. Soc. 196 (1974), 51-67
MSC: Primary 13D15; Secondary 12B20
MathSciNet review: 0344240
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Abstract: Let R be a Noetherian domain with finite integral closure $ \bar R$. We study the map from the Brauer group of $ R,B(R)$, to $ B(\bar R)$: first, by embedding $ B(R)$ into the Čech etale cohomology group $ {H^2}(R,U)$ and using a Mayer-Vietoris sequence for Čech cohomology of commutative rings; second, via Milnor's theorem from algebraic K-theory. We apply our results to show, i.e., that if R is a domain with quotient field K a global field, then the map from $ B(R)$ to $ B(K)$ is 1-1.

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Article copyright: © Copyright 1974 American Mathematical Society