Deligne–Lusztig constructions for division algebras and the local Langlands correspondence, II
نویسندگان
چکیده
منابع مشابه
Deligne–lusztig Constructions for Division Algebras and the Local Langlands Correspondence, Ii
In 1979, Lusztig proposed a cohomological construction of supercuspidal representations of reductive p-adic groups, analogous to Deligne–Lusztig theory for finite reductive groups. In this paper we establish a new instance of Lusztig’s program. Precisely, let X be the Deligne–Lusztig (ind-pro-)scheme associated to a division algebra D over a non-Archimedean local field K of positive characteris...
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Let K be a local non-Archimedean field of positive characteristic and let L be the degree-n unramified extension of K. Let θ be a smooth character of L× such that for each nontrivial γ ∈ Gal(L/K), θ and θ/θ have the same level. Via the local Langlands and Jacquet-Langlands correspondences, θ corresponds to an irreducible representation ρθ of D×, where D is the central division algebra over K wi...
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The local Langlands correspondence for GL(n) of a non-Archimedean local field F parametrizes irreducible admissible representations of GL(n, F ) in terms of representations of the Weil-Deligne group WDF of F . The correspondence, whose existence for p-adic fields was proved in joint work of the author with R. Taylor, and then more simply by G. Henniart, is characterized by its preservation of s...
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In these notes, based on my lectures at the FRG workshop on “Characters, Liftings, and Types” at American University in June 2012, I give an introduction to the conjectural Local Langlands Correspondence (LLC), for split semisimple groups over a nonarchimedean local field. This conjecture has been evolving over the past 45 years (with roots going back much further) to the point that today’s sta...
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The cohomology of the Lubin-Tate tower is known to realize the local Langlands correspondence for GL(n) over a nonarchimedean local field. In this article we make progress towards a purely local proof of this fact. To wit, we find a family of formal schemes V such that the generic fiber of V is isomorphic to an open subset of Lubin-Tate space at infinite level, and such that the middle cohomolo...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2018
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-018-0410-6