Compact sheaves on a locally compact space
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915946329800704 |
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| author | Harr, Oscar |
| author_facet | Harr, Oscar |
| contents | We describe the compact objects in the $\infty$-category of $\mathcal C$-valued sheaves $\text{Shv} (X,\mathcal C)$ on a hypercomplete locally compact Hausdorff space $X$, for $\mathcal C$ a compactly generated stable $\infty$-category. When $X$ is a non-compact connected manifold and $\mathcal C$ is the unbounded derived category of a ring, our result recovers a result of Neeman. Furthermore, for $X$ as above and $\mathcal C$ a nontrivial compactly generated stable $\infty$-category, we show that $\text{Shv} (X,\mathcal C)$ is compactly generated if and only if $X$ is totally disconnected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12127 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compact sheaves on a locally compact space Harr, Oscar Algebraic Topology K-Theory and Homology We describe the compact objects in the $\infty$-category of $\mathcal C$-valued sheaves $\text{Shv} (X,\mathcal C)$ on a hypercomplete locally compact Hausdorff space $X$, for $\mathcal C$ a compactly generated stable $\infty$-category. When $X$ is a non-compact connected manifold and $\mathcal C$ is the unbounded derived category of a ring, our result recovers a result of Neeman. Furthermore, for $X$ as above and $\mathcal C$ a nontrivial compactly generated stable $\infty$-category, we show that $\text{Shv} (X,\mathcal C)$ is compactly generated if and only if $X$ is totally disconnected. |
| title | Compact sheaves on a locally compact space |
| topic | Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2309.12127 |