Points de hauteur bornée, topologie adélique et mesures de Tamagawa

Si $V$ est une variété algébrique projective sur un corps de nombres dont les points rationnels sont denses pour la topologie de Zariski, il est naturel de munir $V$ d’une hauteur et d’étudier de manière asymptotique les points de hauteur bornée sur $V$. Le but de ce texte est de faire le survol d’un programme initié par Manin visant à interpréter de façon géométrique ce comportement.

Let $V$ be a projective algebraic variety over a number field such that the rational points of $V$ are Zariski dense. It is natural to equip $V$ with a height and to study the asymptotic behavior of the points of bounded height on $V$. The purpose of this text is a survey of the program started by Manin which proposes an interpretation of this behavior in terms of the geometry of $V$.

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