D\'evissage for periodic cyclic homology of complete intersections

TL;DR

This paper proves the devissage property for periodic cyclic homology in local complete intersections and establishes isomorphisms for Chern character maps, advancing noncommutative Hodge theory and the Lattice Conjecture.

Contribution

It demonstrates the devissage property for periodic cyclic homology in local complete intersections and confirms the isomorphism of Chern character maps, providing new evidence for the Lattice Conjecture.

Findings

Devissage property holds for periodic cyclic homology in local complete intersections.

Complexified topological Chern character maps are isomorphisms in new cases.

Advances understanding of noncommutative Hodge theory and the Lattice Conjecture.

Abstract

We prove that the d\'evissage 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.