Converse theorems and the local Langlands correspondence in families
File(s)
Published version
Author(s)
Helm, DF
Moss, Gilbert
Type
Journal Article
Abstract
We prove a descent criterion for certain families of smooth representations of GLn(F) (F a p-adic field) in terms of the γ-factors of pairs constructed in Moss (Int Math Res Not 2016(16):4903–4936, 2016). We then use this descent criterion, together with a theory of γ-factors for families of representations of the Weil group WF (Helm and Moss in Deligne–Langlands gamma factors in families, arXiv:1510.08743v3, 2015), to prove a series of conjectures, due to the first author, that give a complete description of the center of the category of smooth W(k)[GLn(F)]-modules (the so-called “integral Bernstein center”) in terms of Galois theory and the local Langlands correspondence. An immediate consequence is the conjectural “local Langlands correspondence in families” of Emerton and Helm (Ann Sci Éc Norm Supér (4) 47(4):655–722, 2014).
Date Issued
2018-11-01
Date Acceptance
2018-07-23
Citation
Inventiones Mathematicae, 2018, 214 (2), pp.999-1022
ISSN
0020-9910
Publisher
Springer Verlag
Start Page
999
End Page
1022
Journal / Book Title
Inventiones Mathematicae
Volume
214
Issue
2
Copyright Statement
© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/M029719/1
Subjects
Science & Technology
Physical Sciences
Mathematics
11F33
11F70
22E50
GL(N)
11F33
11F70
22E50
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2018-09-08