Geodesic
Good reduction of affinoids on the Lubin-Tate tower
Documenta mathematica, Tome 15 (2010), pp. 981-1007
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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 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.
DOI : 10.4171/dm/321
Classification : 11F70, 14G22, 22E50
Mots-clés : Lubin-Tate spaces, local Langlands correspondence, semistable model, rigid analysis 
@article{10_4171_dm_321,
     author = {Jared Weinstein},
     title = {Good reduction of affinoids on the {Lubin-Tate} tower},
     journal = {Documenta mathematica},
     pages = {981--1007},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/321},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/321/}
}
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Jared Weinstein. Good reduction of affinoids on the Lubin-Tate tower. Documenta mathematica, Tome 15 (2010), pp. 981-1007. doi: 10.4171/dm/321

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