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Torseurs arithmetiques et espaces fibres

Antoine Chambert-Loir·Yuri Tschinkel
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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.

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BibTeXRIS

Antoine Chambert-Loir, Yuri Tschinkel. 1999-01-04. Torseurs arithmetiques et espaces fibres. https://arxiv.org/abs/math/9901006

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