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Curtis homomorphisms and the integral Bernstein center for GL_n
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 |