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Proceedings of the American Mathematical Society

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Brauer groups of linear algebraic groups with characters

Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 71 (1978), 164-168
MSC: Primary 13A20; Secondary 14F20, 14L15, 20G15
MathSciNet review: 0485816
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Abstract: Let G be a connected linear algebraic group over an algebraically closed field of characteristic zero. Then the Brauer group of G is shown to be $ C \times {({\mathbf{Q}}/Z)^{(n)}}$ where C is finite and $ n = d(d - 1)/2$, with d the Z-rank of the character group of G. In particular, a linear torus of dimension d has Brauer group $ {({\mathbf{Q}}/Z)^{(n)}}$ with n as above.

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Keywords: Azumaya algebra, algebraic group, Brauer group, étale cohomology
Article copyright: © Copyright 1978 American Mathematical Society