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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.14322 |
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| _version_ | 1866929509721178112 |
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| author | Ji, Caleb Kothari, Casimir Li, Oliver Makarova, Svetlana Sahai, Shubhankar Venkatesh, Sridhar |
| author_facet | Ji, Caleb Kothari, Casimir Li, Oliver Makarova, Svetlana Sahai, Shubhankar Venkatesh, Sridhar |
| contents | Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies to two-term complexes of this type. We apply this to give a new proof of Poincaré duality for relative algebraic de Rham cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality of differential operators and algebraic de Rham cohomology Ji, Caleb Kothari, Casimir Li, Oliver Makarova, Svetlana Sahai, Shubhankar Venkatesh, Sridhar Algebraic Geometry 14F40 Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies to two-term complexes of this type. We apply this to give a new proof of Poincaré duality for relative algebraic de Rham cohomology. |
| title | Duality of differential operators and algebraic de Rham cohomology |
| topic | Algebraic Geometry 14F40 |
| url | https://arxiv.org/abs/2409.14322 |