David Helm
Published 2012-10-05Version 1
We establish integral analogues of results of Bushnell and Henniart for spaces of Whittaker functions arising from the groups GL_n(F) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the conjectural "local Langlands correspondence in families" of Emerton-Helm, and reduce the question of the existence of such representations to a natural conjecture relating the integral Bernstein center of GL_n(F) to the deformation theory of Galois representations.
Reduction of Galois Representations of slope 1
An effective isomorphy criterion for mod $\ell$ Galois representations
On the image of complex conjugation in certain Galois representations
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