77 research outputs found
Theorie de Lubin-Tate non-abelienne et representations elliptiques
Harris and Taylor proved that the supercuspidal part of the cohomology of the
Lubin-Tate tower realizes both the local Langlands and Jacquet-Langlands
correspondences, as conjectured by Carayol. Recently, Boyer computed the
remaining part of the cohomology and exhibited two defects : first, the
representations of GL\_d which appear are of a very particular and restrictive
form ; second, the Langlands correspondence is not realized anymore. In this
paper, we study the cohomology complex in a suitable equivariant derived
category, and show how it encodes Langlands correspondance for all elliptic
representations. Then we transfer this result to the Drinfeld tower via an
enhancement of a theorem of Faltings due to Fargues. We deduce that Deligne's
weight-monodromy conjecture is true for varieties uniformized by Drinfeld's
coverings of his symmetric spaces.Comment: 54 page
On unitarizability in the case of classical p-adic groups
In the introduction of this paper we discuss a possible approach to the
unitarizability problem for classical p-adic groups. In this paper we give some
very limited support that such approach is not without chance. In a forthcoming
paper we shall give additional evidence in generalized cuspidal rank (up to)
three.Comment: This paper is a merged and revised version of ealier preprints
arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the
Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul
Sur la variation, par torsion, des constantes locales d’équations fonctionnelles de fonctions L
info:eu-repo/semantics/publishe
Sur la variation, par torsion, des constantes locales d'équations fonctionelles de fonctions L.
Explicit Jacquet-Langlands correspondence II. The case of degree equal to residual characteristic
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