Automorphic lifts of prescribed types

@article{Gee2011AutomorphicLO,
  title={Automorphic lifts of prescribed types},
  author={Toby Gee},
  journal={Mathematische Annalen},
  year={2011},
  volume={350},
  pages={107-144}
}
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… CONTINUE READING

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