Imperial College London
Professor David Helm

ProfessorDavidHelm

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

d.helm

 
 
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Location

 

672Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Helm:2018:10.1007/s00222-018-0816-y,
author = {Helm, DF and Moss, G},
doi = {10.1007/s00222-018-0816-y},
journal = {Inventiones Mathematicae},
pages = {999--1022},
title = {Converse theorems and the local Langlands correspondence in families},
url = {http://dx.doi.org/10.1007/s00222-018-0816-y},
volume = {214},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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).
AU  - Helm,DF
AU  - Moss,G
DO  - 10.1007/s00222-018-0816-y
EP  - 1022
PY  - 2018///
SN  - 0020-9910
SP  - 999
TI  - Converse theorems and the local Langlands correspondence in families
T2  - Inventiones Mathematicae
UR  - http://dx.doi.org/10.1007/s00222-018-0816-y
UR  - http://hdl.handle.net/10044/1/64383
VL  - 214
ER  -
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