We extend cyclic homology from algebras to all schemes over a ring k.
By `extend' we mean that the usual cyclic homology of any commutative
algebra agrees wth the cyclic homology of its corresponding affine scheme.
There is an appendix showing that the classical Cartan-Eilenberg
hypercohomology of an unbounded chain complex is actually the
hypercohomology in the derived category.
We've removed the original dvi file for this paper. Here is the
revised version.