Abstract:We prove automorphy lifting results for certain essentially conjugate self-dual p-adic Galois representations ρ over CM imaginary fields F , which satisfy in particular that p splits in F , and that the restriction of ρ on any decomposition group above p is reducible with all the Jordan-Hölder factors of dimension at most 2. We also show some results on Breuil's locally analytic socle conjecture in certain non-trianguline case. The main results are obtained by establishing an R = T-type result over the GL 2 (Q… Show more
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