Periodic Cyclic Homology over Q
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914814388862976 |
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| author | Bals, Konrad |
| author_facet | Bals, Konrad |
| contents | Let $X$ be a derived scheme over an animated commutative ring of characteristic 0. We give a complete description of the periodic cyclic homology of $X$ in terms of the Hodge completed derived de Rham complex of $X$. In particular this extends earlier computations of Loday-Quillen to non-smooth algebras. Moreover, we get an explicit condition on the Hodge completed derived de Rham complex, that makes the HKR-filtration on periodic cyclic homology constructed by Antieau and Bhatt-Lurie exhaustive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03112 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Periodic Cyclic Homology over Q Bals, Konrad Algebraic Topology Algebraic Geometry Let $X$ be a derived scheme over an animated commutative ring of characteristic 0. We give a complete description of the periodic cyclic homology of $X$ in terms of the Hodge completed derived de Rham complex of $X$. In particular this extends earlier computations of Loday-Quillen to non-smooth algebras. Moreover, we get an explicit condition on the Hodge completed derived de Rham complex, that makes the HKR-filtration on periodic cyclic homology constructed by Antieau and Bhatt-Lurie exhaustive. |
| title | Periodic Cyclic Homology over Q |
| topic | Algebraic Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2301.03112 |