Patching and the p-adic Langlands program for GL(2)(Q(p))
File(s)1609.06902v2.pdf (563.1 KB)
Accepted version
Author(s)
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.
Date Issued
2018-03-01
Date Acceptance
2017-08-28
Citation
Compositio Mathematica, 2018, 154 (3), pp.503-548
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
Commission of the European Communities
The Leverhulme Trust
Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
Grant Number
FP7-ERC-StG-2012-306326
LH.PZ.GEE.2012
FP7-PEOPLE-2011-CIG-303605
EP/L025485/1
Subjects
Science & Technology
Physical Sciences
Mathematics
p-adic Langlands
local-global compatibility
Taylor-Wiles patching
MODULAR-REPRESENTATIONS
GALOIS REPRESENTATIONS
CONJECTURE
ALGEBRAS
FAMILIES
RINGS
Publication Status
Published