Title: On some local-global compatibility of locally analytic representations

Speaker: Yiwen Ding

Time: May 9, 2013 2:00 pm

Venue: Room 29,Quan Zhai, BICMR

Abstract: Let F be a finite unramified extension of Qp, to a crystalline representation \rho of dimension 2 of Gal(\bar{Q_p}/F), Breuil has associated a locally Qp-analytic representation \Pi(\rho) of GL2(F). And he conjectures that if this \rho is from a Hilbert eigenform, then \Pi(\rho) will occur together with \rho in the p-adically completed cohomology of the tower of certain Shimura curves. In this talk, we will show that it holds for a piece of \Pi(\rho), following the method of Breuil-Emerton.