| Résume | Let F be the function field of a smooth, irreducible projective curve over the reals. Let X be a smooth, projective, geometrically irreducible variety equipped with a dominant morphism f onto a smooth projective rational variety with a smooth generic fibre over F. Assume that the cohomological obstruction introduced by Colliot-Thélène is the only one to the local-global principle for rational points for the smooth fibres of f over F-valued points. I will talk about how to show that the same holds for X, too, by adopting the fibration method. Joint work with Endre Szabó. |
