Correspondances de Langlands locales dans la cohomologie des espaces de Rapoport-Zink

2001/09/26 by Laurent Fargues, Fargues, Laurent
Mathematics · #11Fxx #11G18 #11S37 #14F20 #14G22 #14L05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11Fxx #msc:11G18 #msc:11S37 #msc:14F20 #msc:14G22 #msc:14L05

paper · pdf · doi:10.48550/arxiv.math/0109209

arxiv created 2001/09/26 · arxiv updated 2009/11/30

Abstract

We generalize the work of M. Harris and R. Taylor on the local Langlands correspondence for the linear group over ℚ_p. We prove some cases of the Kottwitz conjectures for the supercuspidal part of the compactly supported ℓ-adic cohomology of Rapoport-Zink rigid-analytic spaces. This means that we decompose this part in terms of local Langlands correspondences. In particular, we prove the first case of a non-abelian reciprocity law constructed geometrically and associated to groups other than inner forms of the linear group. More precisely, we do this for the unramified unitary group in three variables over ℚ_p.

Related

• The Kottwitz conjecture for unitary PEL-type Rapoport--Zink spaces
• Un cas PEL de la conjecture de Kottwitz
• Correspondance locale de Langlands et monodromie des espaces de Drinfeld
• On the local Langlands correspondence
• On the Kottwitz conjecture for local shtuka spaces