On non-abelian Lubin-Tate theory via vanishing cycles
Number Theory
2010-05-20 v3 Algebraic Geometry
Representation Theory
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.
Keywords
Cite
@article{arxiv.math/0404375,
title = {On non-abelian Lubin-Tate theory via vanishing cycles},
author = {Teruyoshi Yoshida},
journal= {arXiv preprint arXiv:math/0404375},
year = {2010}
}
Comments
34 pages, some proofs updated, final version to appear in Advanced Studies in Pure Mathematics, 58 (2010), Algebraic and Arithmetic Structures of Moduli Spaces (Sapporo 2007)