Perfect complexes and completion
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910708730429440 |
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| author | Balmer, Paul Sanders, Beren |
| author_facet | Balmer, Paul Sanders, Beren |
| contents | Let $\hat{R}$ be the $I$-adic completion of a commutative ring $R$ with respect to a finitely generated ideal $I$. We give a necessary and sufficient criterion for the category of perfect complexes over $\hat{R}$ to be equivalent to the subcategory of dualizable objects in the derived category of $I$-complete complexes of $R$-modules. Our criterion is always satisfied when $R$ is noetherian. When specialized to $R$ local and noetherian and to $I$ the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause and Pevtsova. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14761 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perfect complexes and completion Balmer, Paul Sanders, Beren Commutative Algebra Algebraic Topology Category Theory K-Theory and Homology Let $\hat{R}$ be the $I$-adic completion of a commutative ring $R$ with respect to a finitely generated ideal $I$. We give a necessary and sufficient criterion for the category of perfect complexes over $\hat{R}$ to be equivalent to the subcategory of dualizable objects in the derived category of $I$-complete complexes of $R$-modules. Our criterion is always satisfied when $R$ is noetherian. When specialized to $R$ local and noetherian and to $I$ the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause and Pevtsova. |
| title | Perfect complexes and completion |
| topic | Commutative Algebra Algebraic Topology Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2411.14761 |