Cohomology of number fields and analytic pro-$p$-groups

In this work, we are interested in the tame version of the Fontaine–Mazur conjecture. By viewing the pro-$p$-proup $\mathcal G_S$ as a quotient of a Galois extension ramified at $p$ and $S$, we obtain a connection between the conjecture studied here and a question of Galois structure. Moreover, following a recent work of A. Schmidt, we give some evidence of links between this conjecture, the étale cohomology and the computation of the cohomological dimension of the pro-$p$-groups $\mathcal G_S$ that appear.