Torseurs arithmetiques et espaces fibres

Abstract

To study problems involving heights as, eg, Manin's conjecture on the number of points of bounded height on an algebraic variety defined over a number field, it is desirable to have a good normalization of these height functions. We show how one can define these on fiber spaces. The construction uses the notion of an ``arithmetic torsor'', which is the analogue for a general algebraic group of adding a hermitian metric at infinity for vector bundles.