A procdh topology
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917559484284928 |
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| author | Kelly, Shane Saito, Shuji |
| author_facet | Kelly, Shane Saito, Shuji |
| contents | In this article we propose a definition of a procdh topos. We show that it encodes procdh excision, has bounded homotopy dimension and therefore is hypercomplete and admits a conservative family of fibre functors. We also describe the local rings.
As an application, we show that nonconnective $K$-theory is the procdh sheafification of connective $K$-theory, and that the motivic cohomology recently proposed by Elmanto and Morrow is the procdh sheafification of Voevodsky's motivic cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A procdh topology Kelly, Shane Saito, Shuji Algebraic Geometry K-Theory and Homology In this article we propose a definition of a procdh topos. We show that it encodes procdh excision, has bounded homotopy dimension and therefore is hypercomplete and admits a conservative family of fibre functors. We also describe the local rings. As an application, we show that nonconnective $K$-theory is the procdh sheafification of connective $K$-theory, and that the motivic cohomology recently proposed by Elmanto and Morrow is the procdh sheafification of Voevodsky's motivic cohomology. |
| title | A procdh topology |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2401.02699 |