Hochschild homology and the derived de Rham complex revisited

By Arpon Raksit. Selecta Mathematica, 2020

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We characterize two objects by universal property: the derived de Rham complex and Hochschild homology together with its Hochschild–Kostant–Rosenberg (HKR) filtration. This involves endowing these objects with extra structure, built on notions of “homotopy-coherent cochain complex” and “filtered circle action” that we study here. We use these universal properties to give a conceptual proof that the associated graded of the HKR filtration identifies with the derived de Rham complex, as well as to give a new construction of the filtrations on cyclic, negative cyclic, and periodic cyclic homology that relate these invariants to derived de Rham cohomology.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/638d1026504bedde5501805c290a7ecb998d1a0b