Categorical resolutions of filtered schemes
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929730401337344 |
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| author | De Deyn, Timothy |
| author_facet | De Deyn, Timothy |
| contents | We give an alternative proof of the theorem by Kuznetsov and Lunts, stating that any separated scheme of finite type over a field of characteristic zero admits a categorical resolution of singularities. Their construction makes use of the fact that every variety (over a field of characteristic zero) can be resolved by a finite sequence of blow-ups along smooth centres. We merely require the existence of (projective) resolutions. To accomplish this we put the $\mathcal{A}$-spaces of Kuznetsov and Lunts in a different light, viewing them instead as schemes endowed with finite filtrations. The categorical resolution is then constructed by gluing together differential graded categories obtained from a hypercube of finite length filtered schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08330 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Categorical resolutions of filtered schemes De Deyn, Timothy Algebraic Geometry 14A22, 18G80, 14E15 We give an alternative proof of the theorem by Kuznetsov and Lunts, stating that any separated scheme of finite type over a field of characteristic zero admits a categorical resolution of singularities. Their construction makes use of the fact that every variety (over a field of characteristic zero) can be resolved by a finite sequence of blow-ups along smooth centres. We merely require the existence of (projective) resolutions. To accomplish this we put the $\mathcal{A}$-spaces of Kuznetsov and Lunts in a different light, viewing them instead as schemes endowed with finite filtrations. The categorical resolution is then constructed by gluing together differential graded categories obtained from a hypercube of finite length filtered schemes. |
| title | Categorical resolutions of filtered schemes |
| topic | Algebraic Geometry 14A22, 18G80, 14E15 |
| url | https://arxiv.org/abs/2309.08330 |