Mayer-Vietoris sequences and Brauer groups of nonnormal domains
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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.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 196 (1974), 51-67
- MSC: Primary 13D15; Secondary 12B20
- DOI: https://doi.org/10.1090/S0002-9947-1974-0344240-8
- MathSciNet review: 0344240