A pro-cdh topology on formal schemes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916405898641408 |
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| author | Kelly, Shane Saito, Shuji |
| author_facet | Kelly, Shane Saito, Shuji |
| contents | We introduce a pro-cdh topology on formal schemes and prove that the $\infty$-topos of pro-cdh sheaves of spaces has an optimal bound of homotopy dimension. This remedies a defect for a pro-cdh topology on schemes introduced in [KS23]. As an application, we give a topos-theoretic interpretation of Weibel's vanishing of negative K-theory and motivic cohomology of Elmanto and Morrow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A pro-cdh topology on formal schemes Kelly, Shane Saito, Shuji Algebraic Geometry We introduce a pro-cdh topology on formal schemes and prove that the $\infty$-topos of pro-cdh sheaves of spaces has an optimal bound of homotopy dimension. This remedies a defect for a pro-cdh topology on schemes introduced in [KS23]. As an application, we give a topos-theoretic interpretation of Weibel's vanishing of negative K-theory and motivic cohomology of Elmanto and Morrow. |
| title | A pro-cdh topology on formal schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.14295 |