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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: Journal Article
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: 19-Nov-2020
Date of Acceptance: 30-Jun-2020
URI: http://hdl.handle.net/10044/1/70717
DOI: 10.2140/ant.2020.14.2607
ISSN: 1937-0652
Publisher: Mathematical Sciences Publishers (MSP)
Start Page: 2607
End Page: 2645
Journal / Book Title: Algebra and Number Theory
Volume: 14
Issue: 10
Copyright Statement: © 2020 Mathematical Sciences Publishers
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M029719/1
Keywords: Science & Technology
Physical Sciences
Mathematics
Langlands correspondence
modular representation theory
p-adic groups
LOCAL LANGLANDS CORRESPONDENCE
Local Galois Representations
Bernstein Center
General Mathematics
0101 Pure Mathematics
Publication Status: Published
Online Publication Date: 2020-11-19
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics