This talk will present the following recent result of Gaetan Chenevier: Let E be a CM field and S be a finite set of primes of E containing the primes dividing a given prime number l and another prime split above the maximal totally real subfield of E. If E_S denotes the maximal algebraic extension of E which is unramified outside S, then the map from the absolute Galois group of the completion E_u to the Galois group of E_S over E, which is induced by an E-embedding of E_S into the algebraic closure of E_u, is injective.