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On mod p local-global compatibility for GL3(Qp) in the non-ordinary case
Let F / Q be a CM field where p splits completely and r ¯ : Gal ( Q ¯ / F ) → GL 3 ( F ¯ p ) a continuous modular Galois representation. Assume that r ¯ is non-ordinary and non-split reducible (niveau 2) at a place …