Dévissage for periodic cyclic homology of complete intersections

We prove that the dévissage property holds for periodic cyclic homology for a local complete intersection embedding into a smooth scheme.As a consequence, we show that the complexified topological Chern character maps for the bounded derived category and singularity category of a local complete intersection are isomorphisms, proving new cases of the Lattice Conjecture in noncommutative Hodge theory.