On non-abelian Lubin-Tate theory via vanishing cycles
arXiv:math/0404375
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.
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)
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- Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations II: wild case
- Explicit non-abelian Lubin-Tate theory for GL(2)
- Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig varieties
- Non-cuspidality outside the middle degree of l-adic cohomology of the Lubin-Tate tower