Lefschetz operator and local Langlands modulo ℓ: the limit case

Dat, Jean-François

doi:10.2140/ant.2014.8.729

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Lefschetz operator and local Langlands modulo $\ell$: the limit case

Jean-François Dat

Vol. 8 (2014), No. 3, 729–766

DOI: 10.2140/ant.2014.8.729

Abstract

Let $K$ be a finite extension of $ℚ_{p}$ with residue field $F_{q}$ , and let $ℓ$ be a prime such that $q \equiv 1 (mod ℓ)$ . We investigate the cohomology of the Lubin–Tate towers of $K$ with coefficients in ${\bar{F}}_{ℓ}$ , and we show how it encodes Vignéras’ Langlands correspondence for unipotent ${\bar{F}}_{ℓ}$ -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

Vol. 8, No. 3, 2014