Geodesic
Complex structure on the smooth dual of $GL(n)$
Documenta mathematica, Tome 7 (2002), pp. 91-112
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Let G denote the p-adic group GL(n), let Π(G) denote the smooth dual of G, let Π(Ω) denote a Bernstein component of Π(G) and let H(Ω) denote a Bernstein ideal in the Hecke algebra H(G). With the aid of Langlands parameters, we equip Π(Ω) with the structure of complex algebraic variety, and prove that the periodic cyclic homology of H(Ω) is isomorphic to the de Rham cohomology of Π(Ω). We show how the structure of the variety Π(Ω) is related to Xi's affirmation of a conjecture of Lusztig for GL(n,C). The smooth dual Π(G) admits a deformation retraction onto the tempered dual Πt(G).
DOI : 10.4171/dm/118
Classification : 11S37, 22E50, 46L80, 46L87
Mots-clés : Langlands correspondence, tempered dual, p-adic GL(n), baum-connes map, smooth dual 
@article{10_4171_dm_118,
     author = {Jacek Brodzki and Roger Plymen},
     title = {Complex structure on the smooth dual of $GL(n)$},
     journal = {Documenta mathematica},
     pages = {91--112},
     year = {2002},
     volume = {7},
     doi = {10.4171/dm/118},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/118/}
}
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Jacek Brodzki; Roger Plymen. Complex structure on the smooth dual of $GL(n)$. Documenta mathematica, Tome 7 (2002), pp. 91-112. doi: 10.4171/dm/118

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