Arithmetic Distance Functions and Height Fuctions in Diophantine Geometry.
Let be a rationally connected algebraic variety, defined over a number field We find a relation between the arithmetic of rational points on and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for -rational points on for all finite extensions (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles of degree...
Nous établissons une version de la conjecture de Manin pour le plan projectif éclaté en trois points alignés, le corps de base étant un corps global de caractéristique positive.