### School of Mathematics and Statistics

### Bernhard Keller

Université Paris 7

### On the cyclic homology of exact categories

**Friday 20th August, 12-1pm, Carslaw 375. **
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 category.

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.