Vol. 8, No. 3, 2014

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Lefschetz operator and local Langlands modulo $\ell$: the limit case

Jean-François Dat

Vol. 8 (2014), No. 3, 729–766
Abstract

Let K be a finite extension of p with residue field Fq, and let be a prime such that q 1(mod). We investigate the cohomology of the Lubin–Tate towers of K with coefficients in F¯, and we show how it encodes Vignéras’ Langlands correspondence for unipotent F¯-representations.

Keywords
local Langlands, Lefschetz operator, modulo $\ell$
Mathematical Subject Classification 2010
Primary: 11S37
Secondary: 11F70, 14G35
Milestones
Received: 18 June 2013
Revised: 7 November 2013
Accepted: 10 December 2013
Published: 31 May 2014
Authors
Jean-François Dat
Institut de Mathématiques de Jussieu
Université Pierre et Marie Curie (Paris 6)
4, place Jussieu
75252 Paris
France