Mixed Hodge structure in cyclic homology and algebraic K-theory. I
type: Item
instance of: scholarly article
title: Mixed Hodge structure in cyclic homology and algebraic K-theory. I
zbMATH Open document ID: 0651.55003
DOI: 10.1007/BF00536977
author: Andrew Nicas
published in: \(K\)-Theory
publication date: 1987-01-01T00:00:00Z
review text: The author studies mixed Hodge structures on multigraded chain complexes (up to quasi-isomorphism). He shows that, if X is a simply-connected quasi-projective complex variety, the reduced Waldhausen K-theory, \(\tilde A_*(X)\), possesses a natural mixed Hodge structure. When X is not simply-connected he constructs a mixed Hodge structure on a quotient of \(\tilde A_*(X)\) by powers of the augmentation ideal in \({\mathbb{Z}}[\pi_ 1(X)]\). Similar results are obtained for the Hochschild and cyclic homology of X. The results are derived from a paper by \textit{R. M. Hain} [Bull. Am. Math. Soc., New Ser. 14, 111-114 (1986; Zbl 0597.55009)] where a mixed Hodge structure is constructed on the homotopy Lie algebra of X.
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 4062143
zbMATH Keywords: Hochschild homology
zbMATH Keywords: mixed Hodge structures on multigraded chain complexes
zbMATH Keywords: simply-connected quasi-projective complex variety
zbMATH Keywords: reduced Waldhausen K-theory
zbMATH Keywords: cyclic homology
zbMATH Keywords: homotopy Lie algebra
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
cites work: Q3758024
cites work: Cyclic homology and algebraic K-theory of spaces. II
cites work: Q3240881
cites work: Iterated path integrals
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cites work: The algebraic topology of smooth algebraic varieties
cites work: Opérations En K-Théorie Algébrique
cites work: Q3048986
full work available at URL: https://doi.org/10.1007/bf00536977
OpenAlex ID: W2083689201
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description: scientific article; zbMATH DE number 4062143