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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2412.18009 |
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| _version_ | 1866910761270378496 |
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| author | Sahoo, Gopinath |
| author_facet | Sahoo, Gopinath |
| contents | We introduce the notion of tensor t-structures on the bounded derived categories of schemes. For a Noetherian scheme $X$ admitting a dualizing complex, Bezrukavnikov-Deligne, and then independently Gabber and Kashiwara have shown that given a monotone comonotone perversity function on $X$ one can construct a t-structure on $\mathbf{D}^b (X)$. We show that such t-structures are tensor t-structures and conversely every tensor t-structure on $\mathbf{D}^b (X)$ arises in this way. We achieve this by first characterising tensor t-structures in terms of Thomason-Cousin filtrations which generalises earlier results of Alonso, Jeremías and Saorín, from Noetherian rings to schemes. We also show that for a smooth projective curve $C$, the derived category $\mathbf{D}^b (C)$ has no non-trivial tensor weight structures, this extends our earlier result on the projective line to higher genus curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor t-structures, perversity functions and weight structures Sahoo, Gopinath Algebraic Geometry 14F08 We introduce the notion of tensor t-structures on the bounded derived categories of schemes. For a Noetherian scheme $X$ admitting a dualizing complex, Bezrukavnikov-Deligne, and then independently Gabber and Kashiwara have shown that given a monotone comonotone perversity function on $X$ one can construct a t-structure on $\mathbf{D}^b (X)$. We show that such t-structures are tensor t-structures and conversely every tensor t-structure on $\mathbf{D}^b (X)$ arises in this way. We achieve this by first characterising tensor t-structures in terms of Thomason-Cousin filtrations which generalises earlier results of Alonso, Jeremías and Saorín, from Noetherian rings to schemes. We also show that for a smooth projective curve $C$, the derived category $\mathbf{D}^b (C)$ has no non-trivial tensor weight structures, this extends our earlier result on the projective line to higher genus curves. |
| title | Tensor t-structures, perversity functions and weight structures |
| topic | Algebraic Geometry 14F08 |
| url | https://arxiv.org/abs/2412.18009 |