Mathematics – K-Theory and Homology
Scientific paper
2005-05-13
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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