Hochschild homology and the derived de Rham complex revisited
Algebraic Geometry
2026-01-21 v3 K-Theory and Homology
Abstract
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.
Keywords
Cite
@article{arxiv.2007.02576,
title = {Hochschild homology and the derived de Rham complex revisited},
author = {Arpon Raksit},
journal= {arXiv preprint arXiv:2007.02576},
year = {2026}
}
Comments
v2: fixed an error in attribution and a few minor mistakes; v3: revised for publication