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Theorie de Lubin-Tate non-abelienne et representations elliptiques

Jean-Francois Dat
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Abstract

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.

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Jean-Francois Dat. 2006-04-03. Theorie de Lubin-Tate non-abelienne et representations elliptiques. https://doi.org/10.1007/s00222-007-0044-3

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