# Traces of Differential Forms and Hochschild Homology

Part of the Lecture Notes in Mathematics book series (LNM, volume 1368)

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1368)

This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms.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.

K-theory algebraic geometry cohomology homology residue

- DOI https://doi.org/10.1007/BFb0098406
- Copyright Information Springer-Verlag Berlin Heidelberg 1989
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-50985-1
- Online ISBN 978-3-540-46125-8
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
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