Vol. 4, No. 3, 2019

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Periodic cyclic homology and derived de Rham cohomology

Benjamin Antieau

Vol. 4 (2019), No. 3, 505–519
Abstract

We use the Beilinson t-structure on filtered complexes and the Hochschild–Kostant–Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme X with graded pieces given by the Hodge completion of the derived de Rham cohomology of X. Such filtrations have previously been constructed by Loday in characteristic zero and by Bhatt–Morrow–Scholze for p-complete negative cyclic and periodic cyclic homology in the quasisyntomic case.

Keywords
negative cyclic homology, periodic cyclic homology, derived de Rham cohomology, $t$-structures, filtered complexes
Mathematical Subject Classification 2010
Primary: 13D03, 14F40
Milestones
Received: 9 October 2018
Revised: 22 March 2019
Accepted: 10 April 2019
Published: 17 December 2019
Authors
Benjamin Antieau
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL
United States