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Automorphic lifts of prescribed types

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Abstract

We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois representation. We prove a result on the structure of deformation rings of local Galois representations, and deduce from this and the method of Khare and Wintenberger a result on the existence of modular lifts of specified type for Galois representations corresponding to Hilbert modular forms of parallel weight 2. We discuss some conjectures on the weights of n-dimensional mod p Galois representations. Finally, we use recent work of Taylor to prove level raising and lowering results for n-dimensional automorphic Galois representations.

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Gee, T. Automorphic lifts of prescribed types. Math. Ann. 350, 107–144 (2011). https://doi.org/10.1007/s00208-010-0545-z

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  • DOI: https://doi.org/10.1007/s00208-010-0545-z

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