On the vanishing of Hochschild homology of locally complete intersections
type: Item
instance of: scholarly article
title: On the vanishing of Hochschild homology of locally complete intersections
zbMATH Open document ID: 0697.14035
DOI: 10.1007/BF01446559
author: Antonio G. Rodicio
author: Javier Majadas
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164768
review text: Let K be a field of characteristic zero, let A be a locally complete intersection K-algebra, and let \(H_ n(A,A)\) denote the Hochschild homology of A. We prove that there exists a convergent spectral sequence \[ E^ 2_{p,q}=H_ p(A,A)\otimes_ A\bigwedge^ qJ/J^ 2 \Rightarrow A\otimes_ R\Omega^ n_{R| K}, \] where R is a polynomial K-algebra of finite type such that \(A=R/J\). We use it to obtain the following result: If \(H_ n(A,A)=0\) for n sufficiently large, then A is a smooth K-algebra.
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 55T05
Mathematics Subject Classification ID: 12G99
zbMATH DE Number: 4142212
zbMATH Keywords: locally complete intersection
zbMATH Keywords: Hochschild homology
zbMATH Keywords: convergent spectral sequence
MaRDI profile type: Publication
cites work: Q4771408
cites work: Q5730198
cites work: Q3240881
cites work: Q5533288
cites work: Q5642708
cites work: Smooth algebras and vanishing of Hochschild homology
OpenAlex ID: W2022758873
description: scientific article; zbMATH DE number 4142212