On non-abelian Lubin-Tate theory via vanishing cycles

By Teruyoshi Yoshida. 2004

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c14ce36535f62d0aa06e69adbd4700fbd6d0dbf5