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 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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