We construct a natural filtration on
-local
topological cyclic homology for any animated commutative rings using prismatic
cohomology and descent theory. In the course of the construction, we also study
some general properties of prismatic cohomology complexes over perfect
prisms after inverting distinguished generators. The construction is intrinsic to
topological cyclic homology and recovers Thomason’s spectral sequence for
-local
algebraic K-theory via the cyclotomic trace map; as a consequence, we also recover
the étale comparison for prismatic cohomology.