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VOL. 58 | 2010 On non-abelian Lubin–Tate theory via vanishing cycles

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 $GL_n$ is realized in the vanishing cycle cohomology of the deformation spaces of one-dimensional formal modules of height $n$. Our proof is given by establishing the direct geometric link with the Deligne–Lusztig theory for $GL_n (\mathbb{F}_q)$.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1257.11103
MathSciNet: MR2676163

Digital Object Identifier: 10.2969/aspm/05810361

Subjects:
Primary: 11S37
Secondary: 11G18, 20C33, 22E50

Rights: Copyright © 2010 Mathematical Society of Japan

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