Some Fréchet algebras for which the Chern character is an isomorphism
Abstract
Description
Using similarities between topological $K$-theory and periodic cyclic homology we show that, after tensoring with $\mathbb C$, for certain Fréchet algebras the Chern character provides an isomorphism between these functors. This is applied to prove that the Hecke algebra and the Schwartz algebra of a reductive $p$-adic group have isomorphic periodic cyclic homology.
The main theorem in the first version was incorrect for algebras related to noncompact manifolds. This has no effect on the results concerning p-adic groups.
In the appendix we show that an analogous cohomological result does hold in the noncompact case.
17 pages, in the third version an appendix was added
17 pages, in the third version an appendix was added