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Patching and the p-adic Langlands program for GL(2)(Q(p))

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Title: Patching and the p-adic Langlands program for GL(2)(Q(p))
Authors: Caraiani, A
Emerton, M
Gee, T
Geraghty, D
Paskunas, V
Shin, SW
Item Type: Journal Article
Abstract: We present a new construction of the -adic local Langlands correspondence for via the patching method of Taylor–Wiles and Kisin. This construction sheds light on the relationship between the various other approaches to both the local and the global aspects of the -adic Langlands program; in particular, it gives a new proof of many cases of the second author’s local–global compatibility theorem and relaxes a hypothesis on the local mod representation in that theorem.
Issue Date: 1-Mar-2018
Date of Acceptance: 28-Aug-2017
URI: http://hdl.handle.net/10044/1/64360
DOI: https://dx.doi.org/10.1112/S0010437X17007606
ISSN: 0010-437X
Publisher: Foundation Compositio Mathematica
Start Page: 503
End Page: 548
Journal / Book Title: Compositio Mathematica
Volume: 154
Issue: 3
Copyright Statement: © The Authors 2017. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor/Funder: Commission of the European Communities
The Leverhulme Trust
Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: FP7-ERC-StG-2012-306326
LH.PZ.GEE.2012
FP7-PEOPLE-2011-CIG-303605
EP/L025485/1
Keywords: Science & Technology
Physical Sciences
Mathematics
p-adic Langlands
local-global compatibility
Taylor-Wiles patching
MODULAR-REPRESENTATIONS
GALOIS REPRESENTATIONS
CONJECTURE
ALGEBRAS
FAMILIES
RINGS
math.NT
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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