Resumen de On Serre's reciprocity conjecture for 2-dimensional mod p representations of Gal(Q/Q)

Chandrashekhar Khare, Jean-Pierre Wintenberger

• 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.