Deformations of polarized automorphic Galois representations and adjoint Selmer groups

@inproceedings{Allen2016DeformationsOP,
  title={Deformations of polarized automorphic Galois representations and adjoint Selmer groups},
  author={Patrick Brodie Allen},
  year={2016}
}
We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic zero point induced from the automorphic representation is formally smooth of the correct dimension. We… CONTINUE READING

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