Holonomic étale sheaves are constructible
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912061949214720 |
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| author | Abbes, Ahmed Saito, Takeshi |
| author_facet | Abbes, Ahmed Saito, Takeshi |
| contents | Building on Beilinson's work, ``constructible sheaves are holonomic,'' we introduce the notion of holonomicity for étale sheaves, without assuming a priori constructibility. Over a perfect base field, we establish the converse of Beilinson's result, showing that holonomic sheaves are indeed constructible. This can be seen as an étale analogue of Kashiwara's theorem on holonomic ${\mathcal D}_X$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holonomic étale sheaves are constructible Abbes, Ahmed Saito, Takeshi Algebraic Geometry 14F20 Building on Beilinson's work, ``constructible sheaves are holonomic,'' we introduce the notion of holonomicity for étale sheaves, without assuming a priori constructibility. Over a perfect base field, we establish the converse of Beilinson's result, showing that holonomic sheaves are indeed constructible. This can be seen as an étale analogue of Kashiwara's theorem on holonomic ${\mathcal D}_X$-modules. |
| title | Holonomic étale sheaves are constructible |
| topic | Algebraic Geometry 14F20 |
| url | https://arxiv.org/abs/2410.04677 |