Decomposition of the Hochschild and cyclic homology of commutative differential graded algebras
type: Item
instance of: scholarly article
title: Decomposition of the Hochschild and cyclic homology of commutative differential graded algebras
zbMATH Open document ID: 0771.13006
DOI: 10.1016/0022-4049(92)90045-H
author: G. Cortiñas
author: Jorge A. Guccione
author: Juan J. Guccione
published in: Journal of Pure and Applied Algebra
publication date: 1993-05-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13N99
zbMATH DE Number: 166155
zbMATH Keywords: differential graded algebras
zbMATH Keywords: Hochschild homology
zbMATH Keywords: cyclic homology
zbMATH Keywords: complete intersection
reviewed by: Lucian Bădescu
MaRDI profile type: Publication
cites work: Q3818418
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cites work: The Hochschild Homology of Complete Intersections
description: scientific article; zbMATH DE number 166155