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arXiv · 1805.00590

The cohomological Brauer group of a torsion $\mathbb{G}_{m}$-gerbe

Minseon Shin
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Abstract

Let $S$ be a scheme and let $\pi : \mathcal{G} \to S$ be a $\mathbb{G}_{m,S}$-gerbe corresponding to a torsion class $[\mathcal{G}]$ in the cohomological Brauer group $\mathrm{Br}'(S)$ of $S$. We show that the cohomological Brauer group $\mathrm{Br}'(\mathcal{G})$ of $\mathcal{G}$ is isomorphic to the quotient of $\mathrm{Br}'(S)$ by the subgroup generated by the class $[\mathcal{G}]$. This is analogous to a theorem proved by Gabber for Brauer-Severi schemes.

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Minseon Shin. 2018-05-02. The cohomological Brauer group of a torsion $\mathbb{G}_{m}$-gerbe. https://arxiv.org/abs/1805.00590

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