### On the cyclic homology of exact categories, by Bernhard Keller

The cyclic homology of an exact category was defined by R. McCarthy using the
methods of F. Waldhausen. McCarthy's theory enjoys a number of desirable
properties, the most basic being the extension property, i.e. the fact that
when applied to the category of finitely generated projective modules over an
algebra it specializes to the cyclic homology of the algebra.

However, we show that McCarthy's theory cannot be both, compatible with
localizations and invariant under functors inducing equivalences in the
derived categories.

This is our motivation for introducing a new theory for which all three
properties hold: extension, invariance and localization. Thanks to these
properties, the new theory can be computed explicitly for a number of
categories of modules and sheaves.

Bernhard Keller <keller@math.jussieu.fr>