A note on Taylor’s Brauer group

S. Caenepeel and F. Grandjean

Vol. 186 (1998), No. 1, 13–27

DOI: 10.2140/pjm.1998.186.13

Abstract

We make clear that some of the properties of central separable algebras without unit, as announced by Taylor and Raeburn, are only valid under the assumption that the algebra in question is flat. This leads to the introduction of two possibly different versions of the big Brauer group. Both of them inject into the second étale cohomology group, and one of them is isomorphic to it.

Milestones

Received: 5 March 1997

Revised: 1 August 1997

Published: 1 November 1998