{"paper":{"title":"Cyclic homology of commutative algebras over general ground rings","license":"","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Guillermo Corti\\~nas","submitted_at":"2000-01-26T08:41:44Z","abstract_excerpt":"We consider commutative algebras and chain DG algebras over a fixed commutative ground ring $k$ as in the title. We are concerned with the problem of computing the cyclic (and Hochschild) homology of such algebras via free DG-resolutions $\\Lambda V @>>> A$. We find spectral sequences $$E^2_{p,q}=H_p(\\Lambda V\\otimes\\Gamma^q(dV))\\Rightarrow HH_{p+q}(\\Lambda V)$$ and $${E'}^2_{\\pq}=H_p(\\Lambda V\\otimes\\Gamma^{\\le q}(dV)) \\Rightarrow HC_{p+q}(\\Lambda V)$$ The algebra $\\Lambda V\\otimes\\Gamma(dV)$ is a divided power version of the de Rham algebra; in the particular case when $k$ is a field of chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001145","kind":"arxiv","version":1},"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"}