By Reinhold Hübl

This monograph presents an creation to, in addition to a unification and extension of the printed paintings and a few unpublished principles of J. Lipman and E. Kunz approximately lines of differential kinds and their kinfolk to duality conception for projective morphisms. The technique makes use of Hochschild-homology, the definition of that is prolonged to the class of topological algebras. Many effects for Hochschild-homology of commutative algebras additionally carry for Hochschild-homology of topological algebras. specifically, after introducing a suitable suggestion completion of differential algebras, one will get a usual transformation among differential kinds and Hochschild-homology of topological algebras. strains of differential varieties are of curiosity to every person operating with duality idea and residue symbols. Hochschild-homology is an invaluable software in lots of parts of k-theory. The therapy within reason effortless and calls for simply little wisdom in commutative algebra and algebraic geometry.