Cyclic homology of commutative algebras over arbitrary ground rings, by Guillermo Cortinas

We consider commutative algebras and chain algebras over a fixed commutative ground ring k as in the title. We are concerned with the problem of computing the cyclic (and Hochschild) homology of such algebras via free DG resolutions. We obtain spectral sequences for the homology of free DG algebras, which we show to degenerate in certain cases. These degeneracy results allow us to relate the Hochschild and cyclic homology of complete intersections with crystalline cohomology.

This eleven page paper is a revised, --and, I hope, improved-- version of a very long paper under the same name which I circulated circa 1993.

Guillermo Cortinas <>