Résume | The aim of this talk is to gain more insight in the spectrum of irreducible smooth representations of a reductive p-adic group G. The noncommutative geometer's approach is to compute the ``cohomology'' of this spectrum, even though it is not Hausdorff. There are (at least) three natural candidates for this cohomology: 1) the K-theory of the reduced C*-algebra of G, 2) the periodic cyclic homology of the Harish-Chandra-Schwartz algebra of G, 3) the periodic cyclic homology of the Hecke algebra of G. We will show that these three invariants are naturally isomorphic, and we will explain the representation-theoretic content of this result. We will also discuss the relation with the Baum-Connes conjecture. |