Relative Monoidal Bondal-Orlov
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913565803282432 |
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| author | Sheshmani, Artan Toledo, Angel |
| author_facet | Sheshmani, Artan Toledo, Angel |
| contents | In this article we study a relative monoidal version of the Bondal-Orlov reconstruction theorem. We establish an uniqueness result for tensor triangulated category structures $(\boxtimes,\mathbb{1})$ on the derived category $D^{b}(X)$ of a variety $X$ which is smooth projective and faithfully flat over a quasi-compact quasi-separated base scheme $S$ in the case where the fibers $X_{s}$ over any point $s\in S$ all have ample (anti-)canonical bundles. To do so we construct a stack $Γ$ of dg-bifunctors which parametrize the local homotopical behaviour of $\boxtimes$, and we study some of its properties around the derived categories of the fibers $X_{s}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Monoidal Bondal-Orlov Sheshmani, Artan Toledo, Angel Algebraic Geometry K-Theory and Homology 14F08, 18G80 In this article we study a relative monoidal version of the Bondal-Orlov reconstruction theorem. We establish an uniqueness result for tensor triangulated category structures $(\boxtimes,\mathbb{1})$ on the derived category $D^{b}(X)$ of a variety $X$ which is smooth projective and faithfully flat over a quasi-compact quasi-separated base scheme $S$ in the case where the fibers $X_{s}$ over any point $s\in S$ all have ample (anti-)canonical bundles. To do so we construct a stack $Γ$ of dg-bifunctors which parametrize the local homotopical behaviour of $\boxtimes$, and we study some of its properties around the derived categories of the fibers $X_{s}$. |
| title | Relative Monoidal Bondal-Orlov |
| topic | Algebraic Geometry K-Theory and Homology 14F08, 18G80 |
| url | https://arxiv.org/abs/2410.20942 |