On the derived functor analogy in the Cuntz-Quillen framework for cyclic homology, by Guillermo Cortiñas

Cuntz and Quillen have shown that, if char(k)=0, then periodic cyclic homology may be regarded, in some sense, as the derived functor of (non-commutative) de Rham (co-)homology. The purpose of this paper is to formalize this derived functor analogy. We show that the localization of the category of countably indexed pro-algebras at the class of deformations exists, and that periodic cyclic homology is the derived functor of de Rham (co)homology with respect to this localization. We also compute the derived functor of rational K-theory, and show it is essentially the fiber of the rational Jones-Goodwillie map to negative cyclic homology.

This paper has appeared in Alg. Colloquium vol. 5, no. 3 (1998) 305-328, so has been removed from this server at the request of the author.

Guillermo Cortiñas <willie@mate.unlp.edu.ar>