{"paper":{"title":"A Hochschild-Kostant-Rosenberg theorem for cyclic homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Iver Ottosen, Marcel B\\\"okstedt","submitted_at":"2016-01-27T15:39:26Z","abstract_excerpt":"Let $A$ be a commutative algebra over the field ${\\mathbb F}_2 = {\\mathbb Z}/2$. We show that there is a natural algebra homomorphism $\\ell (A) \\to HC^-_*(A)$ which is an isomorphism when $A$ is a smooth algebra. Thus, the functor $\\ell$ can be viewed as an approximation of negative cyclic homology and ordinary cyclic homology $HC_*(A)$ is a natural $\\ell (A)$-module. In general, there is a spectral sequence $E^2 = L_*(\\ell )(A) \\Rightarrow HC_*^- (A)$. We find associated approximation functors $\\ell^+$ and $\\ell^{per}$ for ordinary cyclic homology and periodic cyclic homology, and set up thei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07412","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}