Cyclic homology, cdh-cohomology and negative K-theory

Pro cdh-descent for cyclic homology and K-theory

In this paper we prove that cyclic homology, topological cyclic homology, and algebraic K-theory satisfy a pro Mayer–Vietoris property with respect to abstract blow-up squares of varieties, in both zero and finite characteristic. This may be interpreted as the well-definedness of K-theory with compact support.

Infinitesimal Cohomology and the Chern Character to Negative Cyclic Homology

There is a Chern character from K-theory to negative cyclic homology. We show that it preserves the decomposition coming from Adams operations, at least in characteristic zero.

Detecting K-theory by Cyclic Homology

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

An Introduction to K -theory and Cyclic Cohomology

Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas

For an algebra B with an action of a Hopf algebra H we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg’s theorem relating...