Geodesic
Good reduction of affinoids on the Lubin-Tate tower
Documenta mathematica, Tome 15 (2010), pp. 981-1007.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\ell$-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 $L$-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.
Classification : 14G22, 22E50, 11F70
Keywords: Lubin-Tate spaces, local Langlands correspondence, semistable model, rigid analysis 
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     author = {Weinstein, Jared},
     title = {Good reduction of affinoids on the {Lubin-Tate} tower},
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     volume = {15},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2010__15__a3/}
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Weinstein, Jared. Good reduction of affinoids on the Lubin-Tate tower. Documenta mathematica, Tome 15 (2010), pp. 981-1007. http://geodesic.mathdoc.fr/item/DOCMA_2010__15__a3/