Relative Brauer Groups and \'etale cohomology

Vivek Sadhu

Relative Brauer Groups and \'etale cohomology

Algebraic Geometry 2020-05-05 v2

Authors: Vivek Sadhu

Abstract

In this article, we construct a natural group homomorphism $\psi: \text{Br}(f)\to H^{1}_{et}(S, f_{*}\mathcal{O}_{X}^{\times}/\mathcal{O}_{S}^{\times})$ for a faithful affine map $f: X \to S$ of noetherian schemes. Here $\text{Br}(f)$ denotes the relative Brauer group of $f.$ We also discuss the behavior of Brauer groups for a subintegral map. Furthermore, we prove a relative version of Kummer's exact sequence.

Keywords

relative brauer group etale cohomology noetherian schemes faithful affine map subintegral map kummer exact sequence

Cite

@article{arxiv.1906.10846,
  title  = {Relative Brauer Groups and \'etale cohomology},
  author = {Vivek Sadhu},
  journal= {arXiv preprint arXiv:1906.10846},
  year   = {2020}
}

Comments

Some changes made due to referee report. Final version and accepted for publication

Relative Brauer Groups and \'etale cohomology

Abstract

Keywords

Cite

Comments

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