Relèvement global d'extensions locales: Quelques problèmes de plongement

Let L/K be a finite Galois extension of p-adic fields, and let F be a totally real number field, with a place v where the completion Fv is isomorphic to K. When p is odd, we show that there exists a totally real finite Galois extension E of F, of same degree over F as L over K, and with its completion Ev isomorphic to L; when p = 2, we have a weaker result. All this plays a rôle in a proof of the Langlands conjectures for GLn over p-adic fields. © Springer-Verlag 2000.