On the transitivity of regular differential forms
type: Item
instance of: scholarly article
title: On the transitivity of regular differential forms
zbMATH Open document ID: 0704.13004
DOI: 10.1007/BF01168300
author: Reinhold Hübl
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155435
review text: Let R/k and S/R be generically smooth algebras of finite type which are equidimensional of relative dimensions d, resp. n. The author proves that the canonical isomorphism of the meromorphic differential forms \({\mathcal M}(\Omega^ d_{R/k})\otimes_ R{\mathcal M}(\Omega^ n_{S/R})\to {\mathcal M}(\Omega^{d+n}_{S/k})\) always induces a morphism of the regular differential forms in the sense of Kunz and Waldi \(\phi:\;\omega^ d_{R/k}\otimes_ R\omega^ n_{S/R}\to \omega^{d+n}_{S/k},\) and that \(\phi\) is an isomorphism in the following two cases: (1) R/k and S/R are both Cohen-Macaulay algebras (2) R/k is a Gorenstein algebra. (A short description of the construction of the regular differential forms of the highest degree is given in a preliminary paragraph.) An example is given, showing that \(\phi\) need not always be an isomorphism.
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 13N05
zbMATH DE Number: 4154583
zbMATH Keywords: meromorphic differential forms
zbMATH Keywords: regular differential forms
zbMATH Keywords: Cohen- Macaulay algebras
zbMATH Keywords: Gorenstein algebra
reviewed by: Robert W. Berger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4154583