Overview

This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms. The approach uses Hochschild-homology, the definition of which is extended to the category of topological algebras. Many results for Hochschild-homology of commutative algebras also hold for Hochschild-homology of topological algebras. In particular, after introducing an appropriate notion of completion of differential algebras, one gets a natural transformation between differential forms and Hochschild-homology of topological algebras. Traces of differential forms are of interest to everyone working with duality theory and residue symbols. Hochschild-homology is a useful tool in many areas of k-theory. The treatment is fairly elementary and requires only little knowledge in commutative algebra and algebraic geometry.

Full Product Details

Author:   Reinhold Hübl
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1989 ed.
Volume:   1368
Dimensions:   Width: 15.50cm , Height: 0.60cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783540509851

ISBN 10:   3540509852
Pages:   118
Publication Date:   22 March 1989
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

The Hochschild homology and the Hochschild cohomology of a topological algebra.- Differential forms and Hochschild homology.- Traces in Hochschild homology.- Traces of Differential Forms.- Traces in complete intersections.- The topological residue homomorphism.- Trace formulas for residues of differential forms.

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