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Abstract
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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
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Mathematical Subject Classification
Primary: 19D55
Secondary: 13D03, 13D09, 14F08
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Milestones
Received: 21 December 2023
Revised: 26 April 2024
Accepted: 12 May 2024
Published: 18 August 2024
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