2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59657Fontaine and Mazur conjecture that a number field k has no infinite unramified Galois extension such that its Galois group is a p-adic analytic pro-p-group. We consider this conjecture for the maximal unramified p-extension of a CM-field k.Number Theorytext