On non-abelian Lubin-Tate theory via vanishing cycles

2004/04/21 by Teruyoshi Yoshida, Yoshida, Teruyoshi
Mathematics · #11G18 #11S37 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0404375

openalex publication_date 2004/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a purely local proof, in the depth 0 case, of the result by Harris-Taylor which asserts that the local Langlands correspondence for GL_n over a p-adic field K realizes itself inside the vanishing cycle cohomology of the deformation space of formal O_K-modules of height n. Our proof is given by establishing the direct geometric link with the Deligne-Lusztig theory for GL_n over the residue field.

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