Picard group action on the category of twisted sheaves

Abstract: In this talk, I will discuss the category of twisted sheaves on a scheme $X$. Let $\mathcal{M}$ be a quasi-coherent sheaf on $X$, and $\alpha$ in $\mathrm{Br}(X)$. We show that the functor $ - \otimes_{\mathcal{O}_X} \mathcal{M} : \operatorname{QCoh}(X, \alpha) \to \operatorname{QCoh}(X, \alpha) $ is naturally isomorphic to the identity functor if and only if $\mathcal{M}\cong \mathcal{O}_{X}$. As a corollary, the action of $\operatorname{Pic}(X)$ on $D^{b}(X, \alpha)$ is faithful for any Noetherian scheme $X$. We also show that taking Brauer twists of varieties does not yield new Calabi--Yau categories. This is joint work with Ting Gong and Yeqin Liu.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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