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