Patching and the p-adic local Langlands correspondence

@article{Caraiani2013PatchingAT,
  title={Patching and the p-adic local Langlands correspondence},
  author={A. Caraiani and M. Emerton and T. Gee and D. Geraghty and Vytautas Pa{\vs}kūnas and S. Shin},
  journal={arXiv: Number Theory},
  year={2013}
}
We use the patching method of Taylor--Wiles and Kisin to construct a candidate for the p-adic local Langlands correspondence for GL_n(F), F a finite extension of Q_p. We use our construction to prove many new cases of the Breuil--Schneider conjecture.