## Local-Global Compatibility in the p-Adic Langlands Program for GL(2) over Q

Matthew Emerton
Northwestern University
November 2, 2010

I will outline the proof of various cases of the local-global compatibility statement alluded to in the title, and also explain its applications to the Fontaine—Mazur conjecture, and to a conjecture of Kisin.

## Local-Global Compatibility in the p-Adic Langlands Progra for GL(2) over Q

Matthew Emerton
Northwestern University
November 3, 2010

I will outline the proof of various cases of the local-global compatibility statement alluded to in the title, and also explain its applications to the Fontaine--Mazur conjecture, and to a conjecture of Kisin.

## Lecture 4

Pierre Colmez
National Center for Scientific Research; Member, School of Mathematics
November 4, 2010

## A Satake Isomorphism $mod.p$

Guy Henniart
University of Paris-Sud
November 4, 2010