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Periodic Cyclic Homology over Q

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arxiv 2301.03112 v2 pith:AR5I4NUL submitted 2023-01-08 math.AT math.AG

Konrad Bals This is my paper · ORCID
classification math.ATmath.AG
keywords cyclicderivedhomologyperiodiccompletedcomplexhodgerham
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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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  1. Motivic cohomology of mixed characteristic schemes

    math.AG 2024-12 conditional novelty 7.0 of 10

    A new non-A1-invariant motivic cohomology for qcqs schemes over Z is built from a global filtration on topological cyclic homology and is shown to relate to algebraic K-theory, étale cohomology, and syntomic cohomology.

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