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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.10407 |
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| _version_ | 1866910627106127872 |
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| author | Park, Doosung |
| author_facet | Park, Doosung |
| contents | In the category of log schemes, it is unclear how to define the blow-ups for non-strict closed immersions. In this article, we introduce the notion of divided log spaces. We obtain the category of divided log spaces by locally inverting log blow-ups in the category of log schemes. We show that blow-ups exist for closed immersions of log smooth divided log spaces. This is an ingredient of the motivic six-functor formalism for log schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10407 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inverting log blow-ups in log geometry Park, Doosung Algebraic Geometry 14A21 In the category of log schemes, it is unclear how to define the blow-ups for non-strict closed immersions. In this article, we introduce the notion of divided log spaces. We obtain the category of divided log spaces by locally inverting log blow-ups in the category of log schemes. We show that blow-ups exist for closed immersions of log smooth divided log spaces. This is an ingredient of the motivic six-functor formalism for log schemes. |
| title | Inverting log blow-ups in log geometry |
| topic | Algebraic Geometry 14A21 |
| url | https://arxiv.org/abs/2303.10407 |