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Peer-reviewedCC BYSelecta Mathematica

Hochschild homology and the derived de Rham complex revisited

  • Arpon Raksit1
  1. 1Northwestern University, Evanston, United States
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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.

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Cite

BibTeXRIS
BibTeX
@article{raksit2026hochschild,
  title = {{Hochschild homology and the derived de Rham complex revisited}},
  author = {Arpon Raksit},
  journal = {Selecta Mathematica},
  year = {2026},
  month = jun,
  doi = {10.1007/s00029-026-01154-w},
  url = {https://doi.org/10.1007/s00029-026-01154-w},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Hochschild homology and the derived de Rham complex revisited
AU  - Arpon Raksit
PY  - 2026
DA  - 2026/06/22
JO  - Selecta Mathematica
DO  - 10.1007/s00029-026-01154-w
UR  - https://doi.org/10.1007/s00029-026-01154-w
AB  - 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.
SN  - 1022-1824
SN  - 1420-9020
ER  -