Lifting low dimensional local systems

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A long-standing conjecture predicts the existence of lifts for Galois representations with F_p coefficients to p-adic coefficients. The case 2-dimensional representations of the absolute Galois group of Q is closely related to Serre's modularity conjecture, proved by Khare and Witenberger. After some recollection on the state of the art about this problem, i will develop the machinery underneath the notion of smooth profinite groups. We will then show how this machinery allows to prove some lifting theorems for low dimensional Galois representations and local systems, getting out of the classical arithmetic world usually considered for this conjecture.