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Centre de Bernstein stable et conjecture d'Aubert-Baum-Plymen-Solleveld

Abstract : This thesis focus on links between the local Langlands correspondence and the Bernstein center. A framework was introduced by Vogan and developed by Haines : the stable Bernstein center. We start by extending the generalized Springer correspondence to the orthogonal group (which is disconnected). Then we state a conjecture about (complete) Langlands parameters of supercuspidal representations of a p-adic split group and we prove it for classical and linear groups thanks to the work of M\oe glin, Henniart and Harris and Taylor. Based on the work of Lusztig on generalized Springer correspondence, we define a cuspidal support map for complete Langlands parameters. Referring to some results of Heiermann, we get a Langlands parametrization of the smooth dual of classical groups. Moreover, we state "Galois" version of the Aubert-Baum-Plymen-Solleveld conjecture and we prove that with the previous results. It gives a new proof of the validity of the ABPS conjecture for classical groups and it provides explicit relations with Langlands correspondence. As a corrolary, we obtain the compatibility of the Langlands correspondence with parabolic induction for classical groups.
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Submitted on : Monday, August 24, 2015 - 11:53:08 AM
Last modification on : Saturday, March 28, 2020 - 2:05:58 AM
Document(s) archivé(s) le : Wednesday, November 25, 2015 - 12:40:02 PM


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  • HAL Id : tel-01186086, version 1


Ahmed Moussaoui. Centre de Bernstein stable et conjecture d'Aubert-Baum-Plymen-Solleveld. Mathématiques générales [math.GM]. Université Pierre et Marie Curie - Paris VI, 2015. Français. ⟨NNT : 2015PA066108⟩. ⟨tel-01186086⟩



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