Equivariant Brauer and Picard groups and a Chase-Harrison-Rosenberg exact sequences

The classical Chase-Harrison-Rosenberg exact sequence relates the Picard and Brauer groups of a Galois extension S of a commutative ring R to the group cohomology of the Galois group. We associate to each action of a locally compact group G on a locally compact space X two groups which we call the equivariant Picard group and the equivariant Brauer group. We then prove an analogue of the ChaseHarrison-Rosenberg exact sequence in the which the roles of the Picard and Brauer groups are played by their equivariant analogues. (C) 2006 Elsevier Inc. All rights reserved.