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arXiv · 2301.03112

Periodic Cyclic Homology over Q

Konrad Bals
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Abstract

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.

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Konrad Bals. 2023-01-08. Periodic Cyclic Homology over Q. https://doi.org/10.2140/akt.2024.9.119

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