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Dévissage for periodic cyclic homology of complete intersections

Michael K. Brown and Mark E. Walker

Vol. 9 (2024), No. 2, 341–367
Abstract

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.

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Keywords
complete intersection, dévissage, lattice conjecture, periodic cyclic homology, topological K-theory
Mathematical Subject Classification
Primary: 19D55
Secondary: 13D03, 13D09, 14F08
Milestones
Received: 21 December 2023
Revised: 26 April 2024
Accepted: 12 May 2024
Published: 18 August 2024
Authors
Michael K. Brown
Department of Mathematics and Statistics
Auburn University
Auburn, AL
United States
Mark E. Walker
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE
United States