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arXiv · 1906.10846

Relative Brauer Groups and \'etale cohomology

Vivek Sadhu
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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.

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Vivek Sadhu. 2019-06-26. Relative Brauer Groups and \'etale cohomology. https://arxiv.org/abs/1906.10846

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