Good reduction of affinoids on the LubinTate tower
Abstract
We analyze the geometry of the tower of LubinTate deformation spaces, which parametrize deformations of a onedimensional formal module of height h together with level structure. According to the conjecture of DeligneCarayol, these spaces realize the local Langlands correspondence in their ladic 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 LubinTate tower with good reduction equal to a rather curious nonsingular hypersurface, whose equation we present explicitly. Granting a conjecture on the Lfunctions of this hypersurface, we find a link between the conjecture of DeligneCarayol and the theory of BushnellKutzko types, at least for certain class of wildly ramified supercuspidal representations of small conductor.
 Publication:

arXiv eprints
 Pub Date:
 January 2010
 arXiv:
 arXiv:1001.3226
 Bibcode:
 2010arXiv1001.3226W
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 14G22;
 22E50;
 11F70
 EPrint:
 22 pages, published version