This monograph offers an advent to, in addition to a unification and extension of the broadcast paintings and a few unpublished rules of J. Lipman and E. Kunz approximately strains of differential varieties and their kin to duality conception for projective morphisms. The technique makes use of Hochschild-homology, the definition of that's prolonged to the class of topological algebras. Many effects for Hochschild-homology of commutative algebras additionally carry for Hochschild-homology of topological algebras. particularly, after introducing a suitable concept finishing touch of differential algebras, one will get a common transformation among differential kinds and Hochschild-homology of topological algebras. strains of differential kinds are of curiosity to each person operating with duality thought and residue symbols. Hochschild-homology is an invaluable instrument in lots of parts of k-theory. The therapy within reason basic and calls for merely little wisdom in commutative algebra and algebraic geometry.
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