On Adically Complete D-Modules in Characteristic Zero
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916322770681856 |
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| author | Yekutieli, Amnon |
| author_facet | Yekutieli, Amnon |
| contents | Let (X, O_X) be an algebraic manifold in characteristic 0, or an analytic manifold over \C. A standard theorem says that a left D_X-module M, which is coherent as an O_X-module, is locally free. This theorem has a generalization to the adically complete algebraic setting, in a paper by Ogus from 1973.
In the present paper we take a new look at the work of Ogus. We provide a detailed proof of the theorem on D-modules, and extend it to the non-noetherian setting. We also give another proof of an interesting result of Ogus about adically complete modules (slightly extended).
In the Appendix we discuss a related error in a book by Bjork. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Adically Complete D-Modules in Characteristic Zero Yekutieli, Amnon Algebraic Geometry Commutative Algebra Let (X, O_X) be an algebraic manifold in characteristic 0, or an analytic manifold over \C. A standard theorem says that a left D_X-module M, which is coherent as an O_X-module, is locally free. This theorem has a generalization to the adically complete algebraic setting, in a paper by Ogus from 1973. In the present paper we take a new look at the work of Ogus. We provide a detailed proof of the theorem on D-modules, and extend it to the non-noetherian setting. We also give another proof of an interesting result of Ogus about adically complete modules (slightly extended). In the Appendix we discuss a related error in a book by Bjork. |
| title | On Adically Complete D-Modules in Characteristic Zero |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2407.09981 |