Brauer groups of linear algebraic groups with characters

Magid, Andy R.

doi:10.1090/S0002-9939-1978-0485816-6

Brauer groups of linear algebraic groups with characters
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by Andy R. Magid

Proc. Amer. Math. Soc. 71 (1978), 164-168

DOI: https://doi.org/10.1090/S0002-9939-1978-0485816-6

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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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