Equivariant Brauer groups and cohomology

In this paper we present a cohomological description of the equivariant Brauer group relative to a Galois finite extension of fields endowed with the action of a group of operators. This description is a natural generalization of the classic Brauer–Hasse–Noetherʹs theorem, and it is established by means of a three-term exact sequence linking the relative equivariant Brauer group, the 2nd cohomology group of the semidirect product of the Galois group of the extension by the group of operators and the 2nd cohomology group of the group of operators.