Abstract
We use the Beilinson t-structure on filtered complexes and the Hochschild– Kostant–Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme X with graded pieces given by the Hodge completion of the derived de Rham cohomology of X. Such filtrations have previously been constructed by Loday in characteristic zero and by Bhatt– Morrow–Scholze for p-complete negative cyclic and periodic cyclic homology in the quasisyntomic case.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 505-519 |
| Number of pages | 15 |
| Journal | Annals of K-Theory |
| Volume | 4 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2019 |
Funding
We thank Thomas Nikolaus for explaining the interaction of the S1-action and the Hopf element η and Peter Scholze for bringing this problem to our attention. We also benefited from conversations with Dmitry Kaledin and Akhil Mathew about the Beilinson t-structure. Finally, Elden Elmanto generously provided detailed comments on a draft of the paper. This work was supported by NSF Grant DMS-1552766.
Keywords
- Derived de Rham cohomology
- Filtered complexes
- Negative cyclic homology
- Periodic cyclic homology
- T-structures
ASJC Scopus subject areas
- Analysis
- Geometry and Topology