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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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Applications of the algebraic geometry of the Putman–Wieland conjecture
Abstract We give two applications of our prior work toward the Putman–Wieland conjecture. First, we deduce a strengthening of a result of Marković–Tošić on virtual mapping class group actions on the homology of covers. Second, let and let be a finite ‐cover of topological surfaces. We show the virtual action of the mapping class group of on an ‐isotypic component of has nonunitary image.
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- Award ID(s):
- 2102955
- PAR ID:
- 10419908
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Proceedings of the London Mathematical Society
- Volume:
- 127
- Issue:
- 1
- ISSN:
- 0024-6115
- Format(s):
- Medium: X Size: p. 116-133
- Size(s):
- p. 116-133
- Sponsoring Org:
- National Science Foundation
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