The $\mathrm{Br}={\mathrm{Br}}^{\prime }$ question for some classifying stacks

Abstract

In this paper we consider the $\mathrm{Br}={\mathrm{Br}}^{\prime }$ question for classifying stacks by various group schemes. These are algebraic stacks that do not necessarily admit a finite flat cover by a scheme for which $\mathrm{Br}={\mathrm{Br}}^{\prime }$ holds, hence are not amenable to the usual argument of pushing forward a twisted vector bundle. We provide two classes of examples satisfying $\mathrm{Br}\ne {\mathrm{Br}}^{\prime }$ that do not "arise from" the scheme case.