On non-abelian Lubin-Tate theory and analytic cohomology

2014/02/23 by Chojecki, Przemyslaw
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1402.5606

Abstract

We prove that the p-adic local Langlands correspondence for GL₂(Q_p) appears in the etale cohomology of the Lubin-Tate tower at infinity. We use global methods using recent results of Emerton on the local-global compatibility and hence our proof applies to local Galois representations which come via a restriction from global pro-modular Galois representations. We also discuss a folklore conjecture which states that the p-adic local Langlands correspondence appears in the de Rham cohomology of the Lubin-Tate tower (Drinfeld tower). We show that a study of the de Rham cohomology for perfectoid spaces reduces to a study of the analytic cohomology and we state a natural conjecture related to it.

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