  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.
