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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 $${\operatorname{Br}}^{\prime}(S)$$ of $$S$$. We show that the cohomological Brauer group $${\operatorname{Br}}^{\prime}(\mathcal{G})$$ of $$\mathcal{G}$$ is isomorphic to the quotient of $${\operatorname{Br}}^{\prime}(S)$$ 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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This content will become publicly available on January 1, 2026
Vanishing of Brauer classes on K3 surfaces under reduction
Abstract Given a Brauer class on a K3 surface defined over a number field, we prove that there exists infinitely many reductions where the Brauer class vanishes, under certain technical hypotheses, answering a question of Frei–Hassett–Várilly‐Alvarado.
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- Award ID(s):
- 2503815
- PAR ID:
- 10611893
- Publisher / Repository:
- London Mathematical Society
- Date Published:
- Journal Name:
- Journal of the London Mathematical Society
- Volume:
- 111
- Issue:
- 1
- ISSN:
- 0024-6107
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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