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Curtis homomorphisms and the integral Bernstein center for GL_n | David Helm
; | Date: |
2 May 2016 | Abstract: | We describe two conjectures, one strictly stronger than the other, that give
descriptions of the integral Bernstein center for GL_n(F) (that is, the center
of the category of smooth W(k)[GL_n(F)]-modules, for F a p-adic field and k an
algebraically closed field of characteristic l different from p) in terms of
Galois theory. Moreover, we show that the weak version of the conjecture (for m
at most n) implies the strong version of the conjecture. In a companion paper
[HM] we show that the strong conjecture for n-1 implies the weak conjecture for
n; thus the two papers together give an inductive proof of both conjectures.
The upshot is a description of the integral Bernstein center for GL_n in purely
Galois- theoretic terms; previous work of the author shows that such a
description implies the conjectural "local Langlands correspondence in
families" of Emerton and the author. | Source: | arXiv, 1605.0487 | Services: | Forum | Review | PDF | Favorites |
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