Comparaison de la cohomologie des tours de Lubin-Tate et de Drinfeld et correspondance de Jacquet-Langlands geometrique

2006/05/26 by L Fargues, Fargues, Laurent
Mathematics · #14Gxx #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0605683

openalex publication_date 2006/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is the last one about the isomorphism between Lubin-Tate and Drinfeld towers. We prove the existence of an isomorphism between the compactly supported etale cohomology of the Lubin-Tate and Drinfeld towers, and more generally their equivariant cohomology complex. We also prove the existence of a geometric local Jacquet-Langlands correspondence between some equivariant rigid etale sheaves on Gross-Hopkins period space ℙ^n-1 and Drinfeld one Ω.

Related

• De Rham cohomology of Lubin-Tate spaces and Drinfeld spaces
• Cohomologie de de Rham du revêtement modéré de la tour de Lubin-Tate
• L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld : demonstration du resultat principal
• Cohomologie de de Rham du revêtement modéré de l'espace de Drinfeld
• Correspondance locale de Langlands et monodromie des espaces de Drinfeld