On the rigidity of the generalized Koszul complexes with applications to Hochschild homology
type: Item
instance of: scholarly article
title: On the rigidity of the generalized Koszul complexes with applications to Hochschild homology
zbMATH Open document ID: 0809.13009
author: Antonio G. Rodicio
published in: Journal of Algebra
publication date: 1994-08-16T00:00:00Z
review text: This paper is a new step in the saga of papers concerning the vanishing of the Hochschild homology and the smoothness of an algebra. In Comment. Math. Helv. 69, 163-168 (1994), the group BACH (Buenos Aires Cyclic Homology Group) proved a result conjectured by the author: Let \(\kappa\) be a field of characteristic zero and let \(A\) be a commutative \(\kappa\)-algebra of finite type. The vanishing of the Hochschild homology \(H_ * (A,A)\) in an odd and an even degree suffices for \(A\) to be smooth. -- In the present paper the author conjectures that for a field \(\kappa\) of arbitrary characteristic and a \(\kappa\)-algebra \(A\) essentially of finite type, if \(H_ p (A,A) = 0\) for some natural number \(p\), then \(A\) is smooth. Using the relationship between \(H_ * (A,A)\) and the homology of the generalized Koszul complexes, he proves his conjecture for locally complete intersections.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 13D25
zbMATH DE Number: 614212
zbMATH Keywords: smoothness
zbMATH Keywords: vanishing of Hochschild homology
zbMATH Keywords: generalized Koszul complexes
zbMATH Keywords: locally complete intersections
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: jabr.1994.1189
OpenAlex ID: W2065689538
DOI: 10.1006/JABR.1994.1189
description: scientific article; zbMATH DE number 614212