Cyclic homology for schemes, by Charles Weibel

This is a revised version of a paper in the preprint server with the same title. The main result has not changed:

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.

The change is in the appendix, which is a discussion of hypercohomology for unbounded cochain complexes of sheaves. We show that, unlike the bounded below case, the classical (Cartan-Eilenberg) hypercohomology of an unbounded chain complex is different (!) from the ``hyper-derived'' hypercohomology in the derived category sense.

This has appeared in Proceedings of the AMS, 124 (1996), 1655-1662.

Charles Weibel <>