Journal of the Ramanujan Mathematical Society

J. L. Colliot-Thelene ¹, B. E. Kunyavskii ²

Affiliations
1 C.N.R.S. URA D0752, Mathematiques, Batiment 425 Universite de Paris-Sud, F-91405 Orsay, FR
2 Department of Mathematics and Computer Science Bar-Ilan University, 52900 Ramat-Gan, IL

Abstract

Let G be a connected linear algebraic group over a field k of characteristic zero. Let E be a principal homogeneous space under G and let X be a smooth K-compactification of E. Under a hypothesis which covers both the case where G is semi-simple and the case where G is a torus, we give an "algebraic" formula for the Brauer group of X. The proof proceeds by reduction to the case of finite fields.

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