The Brauer group is torsion
HTML articles powered by AMS MathViewer
- by David J. Saltman
- Proc. Amer. Math. Soc. 81 (1981), 385-387
- DOI: https://doi.org/10.1090/S0002-9939-1981-0597646-5
- PDF | Request permission
Abstract:
We present a new proof that if $A$ is an Azumaya algebra over a commutative ring $R$ of rank ${n^2}$, then ${A^n} = A{ \otimes _R} \cdots { \otimes _R}A$ is a split Azumaya algebra ${\text {En}}{{\text {d}}_R}(P)$. We provide a description of $P$, including that it is a direct summand of ${A^n}$.References
- Nathan Bourbaki, Commutative algebra, Addison-Wesley, Reading, Mass., 1972.
- Frank DeMeyer and Edward Ingraham, Separable algebras over commutative rings, Lecture Notes in Mathematics, Vol. 181, Springer-Verlag, Berlin-New York, 1971. MR 0280479
- Alexander Grothendieck, Le groupe de Brauer. I. Algèbres d’Azumaya et interprétations diverses, Dix exposés sur la cohomologie des schémas, Adv. Stud. Pure Math., vol. 3, North-Holland, Amsterdam, 1968, pp. 46–66 (French). MR 244269
- Max-Albert Knus and Manuel Ojanguren, Théorie de la descente et algèbres d’Azumaya, Lecture Notes in Mathematics, Vol. 389, Springer-Verlag, Berlin-New York, 1974 (French). MR 0417149
- David J. Saltman, Norm polynomials and algebras, J. Algebra 62 (1980), no. 2, 333–345. MR 563232, DOI 10.1016/0021-8693(80)90186-6
- Tsuneo Tamagawa, Representation theory and the notion of the discriminant, Algebraic number theory (Kyoto Internat. Sympos., Res. Inst. Math. Sci., Univ. Kyoto, Kyoto, 1976) Japan Soc. Promotion Sci., Tokyo, 1977, pp. 219–227. MR 0485817
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 385-387
- MSC: Primary 16A16; Secondary 13A20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0597646-5
- MathSciNet review: 597646