Torseurs arithmetiques et espaces fibres

Details Torseurs arithmetiques et espaces fibres Torseurs arithmetiques et espaces fibres

1999-01-04

arxiv.org/abs/math/9901006v1

Mathematics

Algebraic Geometry

28 pages

Scientific paper

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.

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