Cyclic homology of hypersurfaces
type: Item
instance of: scholarly article
title: Cyclic homology of hypersurfaces
zbMATH Open document ID: 0767.19003
DOI: 10.1016/0022-4049(92)90044-G
author: BACH (Buenos Aires Cyclic Homology Group)
published in: Journal of Pure and Applied Algebra
publication date: 1993-05-16T00:00:00Z
review text: Let \(A\) be a geometrically regular \(k\)-algebra over a characteristic zero field \(k\) and \(P\in A\) be a nonzero divisor. In [Funkts. Anal. Prilozh. 19, No. 2, 55--62 (1985; Zbl 0585.18007)], \textit{B. L. Feigin} and \textit{B. L. Tsygan} proved that the cyclic homology of \({A\over \langle P\rangle}\) is a direct sum of the homologies of the complexes \(\Omega^*(A)/F_ j\Omega^*(A)\), where \(F_ j\) is a filtration that depends on \(P\). In this paper, the authors compute explicitly the homologies of the complexes \(\Omega^*(A)/F_ j\Omega^*(A)\) in terms of de Rham homologies and differential modules of the \(k\)-algebras \(A/(p^ i)\).
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 13D03
zbMATH DE Number: 166154
zbMATH Keywords: geometrically regular \(k\)-algebra
zbMATH Keywords: homologies of complexes
zbMATH Keywords: cyclic homology
zbMATH Keywords: filtration
zbMATH Keywords: De Rham homologies
zbMATH Keywords: differential modules
reviewed by: Yves Félix
MaRDI profile type: Publication
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full work available at URL: 0022-4049(92)90044-g
OpenAlex ID: W96367760
description: scientific article; zbMATH DE number 166154