Central separable algebras which are locally endomorphism rings of free modules
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- by Bernice L. Auslander PDF
- Proc. Amer. Math. Soc. 30 (1971), 395-404 Request permission
Abstract:
The object of this paper is to study the kernel of the map of the Brauer group of an integrally closed noetherian domain A into the direct product of the Brauer groups of the localizations of A at prime ideals. It is shown that this kernel is isomorphically contained in the torsion subgroup of the first cohomology group of the sheaf of Cartier divisors over Spec A. As a consequence, the author describes several new sets of conditions on A which guarantee that the kernel is trivial.References
- Bernice Auslander, The Brauer group of a ringed space, J. Algebra 4 (1966), 220–273. MR 199213, DOI 10.1016/0021-8693(66)90040-8
- Maurice Auslander and Oscar Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409. MR 121392, DOI 10.1090/S0002-9947-1960-0121392-6
- Maurice Auslander and Oscar Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24. MR 117252, DOI 10.1090/S0002-9947-1960-0117252-7
- N. Bourbaki, Éléments de mathématique. VII. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Chapitre III: Algèbre multilinéaire, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1044, Hermann & Cie, Paris, 1948 (French). MR 0026989 —, Algèbre commutative, Chapitre 7, Hermann, Paris, 1965. A. Grothendieck, Groupes de Brauer, Séminaire Bourbaki 1964/65, Exposé 290, Benjamin, New York, 1966. MR 33 #54201.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 395-404
- MSC: Primary 13.15
- DOI: https://doi.org/10.1090/S0002-9939-1971-0285517-7
- MathSciNet review: 0285517