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  1. (, Annals of mathematics)
    Accepted Manuscript Full Text Available
  2. ; ; ; ; ; ; ; ; ; (, Annals of Mathematics)
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  3. ; (, Forum of Mathematics, Sigma)
    Abstract Let F be a CM number field. We generalise existing automorphy lifting theorems for regular residually irreducible p -adic Galois representations over F by relaxing the big image assumption on the residual representation. 
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  4. (, Inventiones mathematicae)
    We prove potential automorphy results for a single Galois representation 𝐺𝐹→𝐺𝐿𝑛(β„šβŽ―βŽ―βŽ―βŽ―βŽ―π‘™) where F is a CM number field. The strategy is to use the p, q switch trick to go between the p-adic and q-adic realisation of a certain variant of the Dwork motive. We choose this variant to break self-duality shape of the motives, but not the Hodge-Tate weights. Another key result to prove is that certain p-adic representations we choose that come from the Dwork motives is ordinarily automorphic. One input is the automorphy lifting theorem in Allen et al.: (Potential automorphy over CM fields, Cornell University, New York 2018) . 
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