The bigger Brauer group and twisted sheaves

TL;DR

This paper proves that for algebraic stacks with quasiaffine diagonal, the bigger Brauer group coincides with the second etale cohomology group, extending results to schemes using twisted sheaves.

Contribution

It establishes the equality of the bigger Brauer group and etale cohomology for algebraic stacks with quasiaffine diagonal, providing new insights for schemes.

Findings

Bigger Brauer group equals etale cohomology in degree two with G_m coefficients.

Each G_m-gerbe arises from a central separable algebra.

Results extend to schemes using twisted sheaves.

Abstract

Given an algebraic stack with quasiaffine diagonal, we show that each G_m-gerbe comes from a central separable algebra. In other words, Taylor's bigger Brauer group equals the etale cohomology in degree two with coefficients in G_m. This gives new results also for schemes. We use the method of twisted sheaves explored by de Jong and Lieblich.