English

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

Algebraic Geometry 2021-09-08 v1

Abstract

In this paper we consider the Br=Br\mathrm{Br} = \mathrm{Br}' 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 Br=Br\mathrm{Br} = \mathrm{Br}' holds, hence are not amenable to the usual argument of pushing forward a twisted vector bundle. We provide two classes of examples satisfying BrBr\mathrm{Br} \ne \mathrm{Br}' that do not "arise from" the scheme case.

Cite

@article{arxiv.2109.02758,
  title  = {The $\mathrm{Br} = \mathrm{Br}'$ question for some classifying stacks},
  author = {Minseon Shin},
  journal= {arXiv preprint arXiv:2109.02758},
  year   = {2021}
}
R2 v1 2026-06-24T05:44:12.774Z