Brauer groups and quotient stacks

Abstract

A natural question is to determine which algebraic stacks are quotient stacks. In this paper we give some partial answers and relate it to the question of whether, for a scheme X, the natural map from the Brauer group (equivalence classes of Azumaya algebras) to the cohomological Brauer group (the torsion subgroup of H 2 ( X , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] m )) is surjective.