The Hodge Filtration and Cyclic Homology, by Charles A. Weibel

We relate the classical Hodge filtration of a complex algebraic variety to the ``Hodge'' decomposition of its cyclic homology. The periodic cyclic homology of the variety agrees with the Betti cohomology, and the tower of S-maps to cyclic homology determines a filtration. For a smooth projective variety, this is exactly the classical Hodge filtration.

In order to prove these results, it is necessary to set up the machinery of cyclic homology for mixed complexes of sheaves. This is done for all quasi-compact quasi-separated schemes over a base ring k. In characteristic zero, this produces a finite decomposition of each cyclic homology group.

This has appeared in K-theory, 12 (1997), 145-164.

Charles A. Weibel <>