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

摘要

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 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.