MODULARITY LIFTING THEOREMS FOR GALOIS REPRESENTATIONS OF UNITARY TYPE

@inproceedings{Guerberoff2011MODULARITYLT,
  title={MODULARITY LIFTING THEOREMS FOR GALOIS REPRESENTATIONS OF UNITARY TYPE},
  author={Lucio Guerberoff},
  year={2011}
}
We prove modularity lifting theorems for ℓ-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type condition at ℓ. This extends the results of Clozel, Harris and Taylor ([CHT08]), and the subsequent work by Taylor ([Tay08]). The proof uses the Taylor-Wiles method, as improved by Diamond, Fujiwara, Kisin and Taylor, applied to Hecke algebras of unitary groups, and results of Labesse ([Lab]) on stable base change and descent from unitary… CONTINUE READING

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