Proves automorphy lifting for essentially conjugate self-dual p-adic Galois representations over CM fields with reducible local conditions at p (JH factors dim ≤2), via R=T over GL2(Qp)-ordinary families, plus partial results on Breuil's socle conjecture in non-trianguline cases.
Blocks for modp representations of GL 2(Qp)
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$\mathrm{GL}_2(\mathbb{Q}_p)$-ordinary families and automorphy lifting
Proves automorphy lifting for essentially conjugate self-dual p-adic Galois representations over CM fields with reducible local conditions at p (JH factors dim ≤2), via R=T over GL2(Qp)-ordinary families, plus partial results on Breuil's socle conjecture in non-trianguline cases.