Geometry of the smooth dual of GL(n)

Details Geometry of the smooth dual of GL(n) Geometry of the smooth dual of GL(n)

2000-07-17

arxiv.org/abs/math/0007107v1

Mathematics

K-Theory and Homology

7 pages, LaTeX

Scientific paper

10.1016/S0764-4442(00)01618-9

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).

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