Geometry of the smooth dual of GL(n)

Brodzki, J. and Plymen, R. (2000) Geometry of the smooth dual of GL(n). Comptes Rendus de l'Academie des Sciences Series I Mathematics, 331 (3), 213-218. (doi:10.1016/S0764-4442(00)01618-9).

Abstract

Let be the smooth dual of the p -adic group G=GL(n). We create on the structure of a complex algebraic variety. There is a morphism of A(n) onto the Bernstein variety ?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).
Soit A(n) le dual lisse du groupe p -adique G=GL(n). Nous donnons a A(n) la structure d'une variete algebrique complexe. Il existe un morphisme canonique de A(n) sur la variete de Bernstein G qui est injectif sur chaque composante de A(n). Il y a une retraction par deformation de A(n) sur le dual tempere de G. L'homologie cyclique periodique HP0(H(G)) (resp. HP1(H(G)) ) est isomorphe a la cohomologie de de Rham paire (resp. impaire) a support un nombre fini de composantes du dual lisse de G.

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Contributors

Author: J. Brodzki

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