On non-abelian Lubin-Tate theory via vanishing cycles

Details On non-abelian Lubin-Tate theory via vanishing cycles On non-abelian Lubin-Tate theory via vanishing cycles

2004-04-21

arxiv.org/abs/math/0404375v3

Mathematics

Number Theory

34 pages, some proofs updated, final version to appear in Advanced Studies in Pure Mathematics, 58 (2010), Algebraic and Arith

Scientific paper

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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