A Hochschild-Kostant-Rosenberg theorem for cyclic homology

Marcel Bökstedt, Iver Ottosen

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Abstract

Let A be a commutative algebra over the field F 2=Z/2. We show that there is a natural algebra homomorphism ℓ(A)→HC (A) which is an isomorphism when A is a smooth algebra. Thus, the functor ℓ can be viewed as an approximation of negative cyclic homology and ordinary cyclic homology HC (A) is a natural ℓ(A)-module. In general, there is a spectral sequence E 2=L (ℓ)(A)⇒HC (A). We find associated approximation functors ℓ + and ℓ per for ordinary cyclic homology and periodic cyclic homology, and set up their spectral sequences. Finally, we discuss universality of the approximations.

Original languageEnglish
JournalJournal of Pure and Applied Algebra
Volume221
Issue6
Pages (from-to)1458–1493
Number of pages38
ISSN0022-4049
DOIs
Publication statusPublished - Jun 2017

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