The bigger Brauer group is really big

Details The bigger Brauer group is really big The bigger Brauer group is really big

2001-08-20

arxiv.org/abs/math/0108135v3

J. Algebra 262 (2003), 210-225.

Mathematics

Algebraic Geometry

14 pages, minor changes, to appear in J. Algebra

Scientific paper

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 G_m-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 G_m-gerbe comes from a central separable algebra.

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