Rigid Dualizing Complexes over Commutative Rings and their Functorial Properties
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929240755142656 |
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| author | Ornaghi, Mattia Singh, Saurabh Yekutieli, Amnon |
| author_facet | Ornaghi, Mattia Singh, Saurabh Yekutieli, Amnon |
| contents | In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base ring, has a unique rigid dualizing complex. The rigid dualizing complexes have strong functorial properties, allowing us to construct the twisted induction pseudofunctor, which is our ring-theoretic version of the twisted inverse pseudofunctor $f^{!}$. This is the first article of a bigger project, whose final goal is establishing Grothendieck Duality, including global duality for proper maps, for Deligne-Mumford stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07150 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigid Dualizing Complexes over Commutative Rings and their Functorial Properties Ornaghi, Mattia Singh, Saurabh Yekutieli, Amnon Algebraic Geometry Commutative Algebra Category Theory Primary: 14F08. Secondary: 18G80, 13D09, 16E45 In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base ring, has a unique rigid dualizing complex. The rigid dualizing complexes have strong functorial properties, allowing us to construct the twisted induction pseudofunctor, which is our ring-theoretic version of the twisted inverse pseudofunctor $f^{!}$. This is the first article of a bigger project, whose final goal is establishing Grothendieck Duality, including global duality for proper maps, for Deligne-Mumford stacks. |
| title | Rigid Dualizing Complexes over Commutative Rings and their Functorial Properties |
| topic | Algebraic Geometry Commutative Algebra Category Theory Primary: 14F08. Secondary: 18G80, 13D09, 16E45 |
| url | https://arxiv.org/abs/2402.07150 |