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arXiv · 1808.05246

Periodic cyclic homology and derived de Rham cohomology

Benjamin Antieau
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Abstract

We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the Hodge-completion of the derived de Rham cohomology of $X$. Such filtrations have previously been constructed by Loday in characteristic zero and by Bhatt-Morrow-Scholze for $p$-complete negative cyclic and periodic cyclic homology in the quasisyntomic case.

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Benjamin Antieau. 2018-08-15. Periodic cyclic homology and derived de Rham cohomology. https://doi.org/10.2140/akt.2019.4.505

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