Classification and nonexistence for $t$-structures on derived categories of schemes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917500975841280 |
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| author | Clark, Alexander Lank, Pat Manali-Rahul, Kabeer Parker, Chris J. |
| author_facet | Clark, Alexander Lank, Pat Manali-Rahul, Kabeer Parker, Chris J. |
| contents | Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-structures restricting to perfect complexes detects regularity, recovering a theorem of Neeman in the affine case by different methods. Our tools establish local-to-global principles for tensor $t$-structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_08578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification and nonexistence for $t$-structures on derived categories of schemes Clark, Alexander Lank, Pat Manali-Rahul, Kabeer Parker, Chris J. Algebraic Geometry Category Theory 14F08 (primary), 13D09, 13F40, 18G80 Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-structures restricting to perfect complexes detects regularity, recovering a theorem of Neeman in the affine case by different methods. Our tools establish local-to-global principles for tensor $t$-structures. |
| title | Classification and nonexistence for $t$-structures on derived categories of schemes |
| topic | Algebraic Geometry Category Theory 14F08 (primary), 13D09, 13F40, 18G80 |
| url | https://arxiv.org/abs/2404.08578 |