The bigger Brauer group is really big

✍ Scribed by Stefan Schröer

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 173 KB
• Volume: 262
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00026-7

✦ Synopsis

I show that each étale n-cohomology class on noetherian schemes comes from a Čech 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 étale G m -gerbe comes from a coherent 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.