Local-Global Compatibility in p-Adic Langlands for GL_2(Q)

IAS/PU NUMBER THEORY
Topic:Local-Global Compatibility in p-Adic Langlands for GL_2(Q)
Speaker:Matthew Emerton
Affiliation:Northwestern University
Date:Thursday, March 29
Time/Room:5:30pm - 6:30pm/Fine Hall 322, Princeton University

In this talk I will explain some recent results on local-global compatibility for the action of GL_2 of the finite adeles on the p-adically completed cohomology of modular curves, as well as some applications of these results (e.g. to the Fontaine-Mazur conjecture). These results rely for their proof on the existence of a p-adic local Langlands correspondence, recently constructed by Colmez, and I will also spend some time describing Colmez's work.