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Periodic cyclic homology
over $\mathbb{Q}$
Konrad Bals |
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Vol. 9 (2024), No. 1, 119–142
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Abstract |
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Let be a derived scheme over an animated commutative ring of characteristic 0. We give a complete description of the periodic cyclic homology of in terms of the Hodge completed derived de Rham complex of . In particular this extends earlier computations of Loday–Quillen and Feigin–Tsygan to nonsmooth and non-lci 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. |
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Keywords
periodic cyclic homology, Hochschild homology, Hodge
completed derived de Rham complex, derived schemes, Tate
filtration
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Mathematical Subject Classification
Primary: 13D03, 19D55
Secondary: 19E08, 55P42
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Milestones
Received: 5 April 2023
Revised: 3 January 2024
Accepted: 3 January 2024
Published: 25 May 2024
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Authors |
| Konrad Bals | |
| Mathematisches Institut Universität Münster Münster Germany |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
