A Hochschild–Kostant–Rosenberg theorem for cyclic homology
Abstract Let A be a commutative algebra over the field F 2 = Z / 2 Z / 2 . We show that there is a natural algebra homomorphism ℓ ( A ) → H C ⁎ − ( 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 H C ⁎ ( A ) is a natural ℓ ( A ) -module. In general, there is a spectral sequence E 2 = <SUB> L ⁎ ( ℓ ) ( A ) ⇒ H C ⁎ − ( A ) . We find associated approximation functors ℓ + and ℓ p e r for ordinary cyclic homology and periodic cyclic homology, and set up their spectral sequences. Finally, we discuss universality of the approximations.
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