Fontaine–Mazur conjecture in the residually reducible case

Fontaine–Mazur conjecture in the residually reducible case

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Lue Pan, Princeton University
Fine Hall 214

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.