Let denote the -adic group , let denote the smooth dual of , let denote a Bernstein component of and let denote a Bernstein ideal in the Hecke algebra . With the aid of Langlands parameters, we equip with the structure of complex algebraic variety, and prove that the periodic cyclic homology of is isomorphic to the de Rham cohomology of . We show how the structure of the variety is related to Xi's affirmation of a conjecture of Lusztig for . The smooth dual admits a deformation retraction onto the tempered dual .
Cite this article
Jacek Brodzki, Roger Plymen, Complex structure on the smooth dual of . Doc. Math. 7 (2002), pp. 91–112DOI 10.4171/DM/118