A Hochschild-Kostant-Rosenberg theorem for cyclic homology

2016/01/27 by Marcel Bökstedt, Bökstedt, Marcel, Iver Ottosen +1
Mathematics · #18G50 #19D55 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1601.07412

openalex publication_date 2016/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a commutative algebra over the field \mathbb F₂ = \mathbb 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 E² = 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.

Citations

• Relative Algebraic K-Theory and Cyclic Homology

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