|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||Fontaine–Mazur conjecture in the residually reducible case|
|Date:||Thursday, March 1|
|Time/Room:||4:30pm - 5:30pm/Fine Hall 214, Princeton University|
We prove the modularity of some two-dimensional residually reducible p-adic Galois representations over Q under certain hypothesis on the residual representation at p. To do this, we generalize Emerton's local-global compatibility result and devise a patching argument for completed homology in this setting.