Nevanlinna-Cartan theory over function fields and a Diophantine equation.
Noether's problem over an algebraically closed field.
Nombre maximum de points rationnels d'une courbe sur un corps fini
Nombres congruents et courbes elliptiques
Nombres de points des courbes algébriques sur F ...
Non standard arithmetic and application to height functions
Non-existence of points rational over number fields on Shimura curves
Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
Nonstandard arithmetic of function fields over H-convex subfields of *Q.