On non-abelian Lubin-Tate theory via vanishing cycles
Teruyoshi Yoshida
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 GLn over a p-adic field K realizes itself inside the vanishing cycle cohomology of the deformation space of formal OK-modules of height n. Our proof is given by establishing the direct geometric link with the Deligne-Lusztig theory for GLn over the residue field.
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