Picard group action on the category of twisted sheaves
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913987794305024 |
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| author | Gong, Ting Liu, Yeqin Shen, Yu |
| author_facet | Gong, Ting Liu, Yeqin Shen, Yu |
| contents | In this paper, we study the category of twisted sheaves over a scheme $X$. Let $\mathcal{M}$ be a quasi-coherent sheaf on $X$, and $α$ in $\operatorname{Br}(X)$. We show that the functor $ - \otimes_{\mathcal{O}_X} \mathcal{M} : \operatorname{QCoh}(X, α) \to \operatorname{QCoh}(X, α) $ 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 $D^{b}(X, α)$ is faithful for any Noetherian scheme $X$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_09379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Picard group action on the category of twisted sheaves Gong, Ting Liu, Yeqin Shen, Yu Algebraic Geometry 14F22 In this paper, we study the category of twisted sheaves over a scheme $X$. Let $\mathcal{M}$ be a quasi-coherent sheaf on $X$, and $α$ in $\operatorname{Br}(X)$. We show that the functor $ - \otimes_{\mathcal{O}_X} \mathcal{M} : \operatorname{QCoh}(X, α) \to \operatorname{QCoh}(X, α) $ 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 $D^{b}(X, α)$ is faithful for any Noetherian scheme $X$. |
| title | Picard group action on the category of twisted sheaves |
| topic | Algebraic Geometry 14F22 |
| url | https://arxiv.org/abs/2508.09379 |