Mathematics – Number Theory
Scientific paper
2010-01-19
Documenta Mathematica 15 (2010) 981-1007
Mathematics
Number Theory
22 pages, published version
Scientific paper
We analyze the geometry of the tower of Lubin-Tate deformation spaces, which parametrize deformations of a one-dimensional formal module of height h together with level structure. According to the conjecture of Deligne-Carayol, these spaces realize the local Langlands correspondence in their l-adic cohomology. This conjecture is now a theorem, but currently there is no purely local proof. Working in the equal characteristic case, we find a family of affinoids in the Lubin-Tate tower with good reduction equal to a rather curious nonsingular hypersurface, whose equation we present explicitly. Granting a conjecture on the L-functions of this hypersurface, we find a link between the conjecture of Deligne-Carayol and the theory of Bushnell-Kutzko types, at least for certain class of wildly ramified supercuspidal representations of small conductor.
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