Periodic cyclic homology and derived de Rham cohomology

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.