Good reduction of affinoids on the Lubin-Tate tower

  • Jared Weinstein

    Dept. of Mathematics University of California Los Angeles Box 951555 Los Angeles, CA 90095-1555 USA
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We analyze the geometry of the tower of Lubin-Tate deformation spaces, which parametrize deformations of a one-dimensional formal module of height hh together with level structure. According to the conjecture of Deligne-Carayol, these spaces realize the local Langlands correspondence in their \ell-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 LL-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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Jared Weinstein, Good reduction of affinoids on the Lubin-Tate tower. Doc. Math. 15 (2010), pp. 981–1007

DOI 10.4171/DM/321