Some Fréchet algebras for which the Chern character is an isomorphism

Details Some Fréchet algebras for which the Chern character is an isomorphism Some Fréchet algebras for which the Chern character is an isomorphism

2005-05-13

arxiv.org/abs/math/0505282v3

K-Theory 36 (2005), 275--290

Mathematics

K-Theory and Homology

17 pages, in the third version an appendix was added

Scientific paper

Using similarities between topological $K$-theory and periodic cyclic homology we show that, after tensoring with $\mathbb C$, for certain Fr\'echet 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.

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