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

Authors
  • Caraiani, Ana
  • Emerton, Matthew
  • Gee, Toby
  • Geraghty, David
  • Paskunas, Vytautas
  • Shin, Sug Woo
Type
Published Article
Publication Date
Aug 31, 2017
Submission Date
Sep 22, 2016
Identifiers
DOI: 10.1112/S0010437X17007606
Source
arXiv
License
Yellow
External links

Abstract

We present a new construction of the p-adic local Langlands correspondence for GL(2, Q_p) 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 global aspects of the p-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 p representation in that theorem.

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