Edidin, Hassett, Kresch, Vistoli — Brauer Groups And Quotient Stacks (2001)

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 \(H\textasciicircum{ 2} (X,{\Bbb G}_{ m} )\)) is surjective.