Traces of Differential Forms and Hochschild Homology
Series: Lecture Notes in Mathematics; 1368;
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Product details:
- Edition number 1989
- Publisher Springer
- Date of Publication 22 March 1989
- Number of Volumes 1 pieces, Book
- ISBN 9783540509851
- Binding Paperback
- No. of pages118 pages
- Size 235x155 mm
- Weight 454 g
- Language English
- Illustrations VI, 118 p. 0
Categories
Long description:
This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms.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.
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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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