Decomposition of the Hochschild and cyclic homology of commutative differential graded algebras
The starting point of this investigation is a paper by \textit{D. Burghelea} and \textit{M. Vigué-Poirrier} [in Algebraic topology, rational homotopy, Proc. Conf., Louvain-la-Neuve 1986, Lect. Notes Math. 1318, 51-72 (1988; Zbl 0666.13007)], according to which the Hochschild and cyclic homology of a free commutative differential graded \(k\)-algebra (with \(k\) a field of characteristic 0) are the corresponding homologies of a bigraded \(S^ 1\)-chain complex which is simpler than the canonical one. The authors of the paper under review refine some results of the cited paper and then apply them to compute these homologies of the localization of the ring of regular functions of an affine variety that is locally a complete intersection.
scientific article; zbMATH DE number 166155