On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q)

@inproceedings{Khare2009OnSC,
  title={On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q)},
  author={Chandrashekhar Khare and Jean-Pierre Wintenberger},
  year={2009}
}
We prove the existence in many cases of minimally ramified p-adic lifts of 2-dimensional continuous, odd, absolutely irreducible, mod p representations of the absolute Galois group of Q. It is predicted by Serre's conjecture that such representations arise from newforms of optimal level and weight.