Hochschild homology and the derived de Rham complex revisited
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866917210380828672 |
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| author | Raksit, Arpon |
| author_facet | Raksit, Arpon |
| contents | We characterize two objects by universal property: the derived de Rham complex and Hochschild homology together with its Hochschild-Kostant-Rosenberg (HKR) filtration. This involves endowing these objects with extra structure, built on notions of "homotopy-coherent cochain complex" and "filtered circle action" that we study here. We use these universal properties to give a conceptual proof that the associated graded of the HKR filtration identifies with the derived de Rham complex, as well as to give a new construction of the filtrations on cyclic, negative cyclic, and periodic cyclic homology that relate these invariants to derived de Rham cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_02576 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hochschild homology and the derived de Rham complex revisited Raksit, Arpon Algebraic Geometry K-Theory and Homology We characterize two objects by universal property: the derived de Rham complex and Hochschild homology together with its Hochschild-Kostant-Rosenberg (HKR) filtration. This involves endowing these objects with extra structure, built on notions of "homotopy-coherent cochain complex" and "filtered circle action" that we study here. We use these universal properties to give a conceptual proof that the associated graded of the HKR filtration identifies with the derived de Rham complex, as well as to give a new construction of the filtrations on cyclic, negative cyclic, and periodic cyclic homology that relate these invariants to derived de Rham cohomology. |
| title | Hochschild homology and the derived de Rham complex revisited |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2007.02576 |