Nous allons parler de l'obstruction de Brauer-Manin pour les 0-cycles sur les variétés rationnellement connexes, particulièrement sur certaine fibrations au-dessus de l'espace projectif et certaine espaces homogènes.Références: http://arxiv.org/abs/1011.5995 et http://arxiv.org/abs/1107.1634
Given a number field k and a prime number p, we are interested in mixed Artin-Tate-motives M over k and in the ell-adic Galois representations attached to them. With these objects one can associate so-called Tate-Shafarevich groups. Their vanishing is, by construction, the obstruction to certain local-global principles. I will show how Leopoldt's conjecture for k and p follows from the finiteness of these groups.
