Points de hauteur bornée, topologie adélique et mesures de Tamagawa
Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, p. 319-349

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.

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.

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     author = {Peyre, Emmanuel},
     title = {Points de hauteur born\'ee, topologie ad\'elique et mesures de Tamagawa},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     pages = {319-349},
     zbl = {1057.14031},
     mrnumber = {2019019},
     language = {fr},
     url = {http://www.numdam.org/item/JTNB_2003__15_1_319_0}
}
Peyre, Emmanuel. Points de hauteur bornée, topologie adélique et mesures de Tamagawa. Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 319-349. http://www.numdam.org/item/JTNB_2003__15_1_319_0/

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