Geometry of the smooth dual of GL(n)

Abstract

Let A(n) be the smooth dual of the p-adic group G=GL(n). We create on A(n) the structure of a complex algebraic variety. There is a morphism of A(n) onto the Bernstein variety Omega G which is injective on each component of A(n). The tempered dual of G is a deformation retract of A(n). The periodic cyclic homology of the Hecke algebra of G is isomorphic to the periodised de Rham cohomology supported on finitely many components of A(n).

arXiv comment7 pages, LaTeX

Cited by in corpus (3)

• Conjectures about p-adic groups and their noncommutative geometry
• Reduced C*-algebra of the p-adic group GL(n) II
• A geometric counterpart of the Baum-Connes map for GL(n)