An exotic smooth structure on .
On démontre que les surfaces cubiques lisses sur les corps de fonctions d’une courbe sur un corps algébriquement clos de caractéristique vérifient l’approximation faible aux places de bonne réduction. La méthode utilisée imite celle employée par Swinnerton-Dyer [10] dans le cas des corps de nombres.
Let be a projective variety which is covered by rational curves, for instance a Fano manifold over the complex numbers. In this paper, we give sufficient conditions which guarantee that every tangent vector at a general point of is contained in at most one rational curve of minimal degree. As an immediate application, we obtain irreducibility criteria for the space of minimal rational curves.