The bigger Brauer group is really big

الأصل · EN

I show that each etale n-cohomology class on noetherian schemes comes from a Cech cocycle, provided that any n-tuple of points admits an affine open neighborhood. Together with results of Raeburn and Taylor on the bigger Brauer group, this implies that for schemes such that each pair of points admits an affine open neighborhood, any etale Gₘ-gerbe comes from a central separable algebra. Such algebras are nonunital generalizations of Azumaya algebras. I also prove that, on normal noetherian schemes, each Zariski Gₘ-gerbe comes from a central separable algebra.