Curtis homomorphisms and the integral Bernstein center for GL_n

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Title: Curtis homomorphisms and the integral Bernstein center for GL_n
Authors: Helm, D
Item Type: Working Paper
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.
Issue Date: 2-May-2016
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M029719/1
Keywords: Local Galois Representations
Bernstein Center
Publication Status: Submitted
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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