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unpublished ideas of J. Lipman and E. Kunz about traces of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.
General
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