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A Hochschild-Kostant-Rosenberg theorem for cyclic homology

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  • 1601.07412

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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.

OriginalsprogEngelsk
TidsskriftJournal of Pure and Applied Algebra
Vol/bind221
Nummer6
Sider (fra-til)1458–1493
Antal sider38
ISSN0022-4049
DOI
StatusUdgivet - jun. 2017

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