Work

Patching and the -adic Langlands program for

Year: 2017

Type: article

Abstract: We present a new construction of the $p$ -adic local Langlands correspondence for $\operatorname{GL}_{2}(\mathbb{Q}_{p})$ 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 the 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.

Source: Compositio Mathematica

DOI: 10.1112/s0010437x17007606

Authors: Ana Caraiani, Matthew Emerton, Toby Gee, David Geraghty, Vytautas Paškūnas, Sug Woo Shin