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arXiv · 1403.6975

Points de hauteur bornée sur les hypersurfaces lisses de l'espace triprojectif

Teddy Mignot
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Abstract

We prove Batyrev/Manin conjecture for the number of points of bounded height on some smooth hypersurfaces of the triprojective space of tridegree (1,1,1). The constant appearing in the final result is the one conjectured by Peyre. The method used is the one developped by Schindler to study the case of hypersurfaces of biprojective spaces. This method is based on the Hardy-Littlewood circle method. ----- Nous démontrons ici la conjecture de Batyrev/Manin pour le nombre de points de hauteur bornée sur des hypersurfaces de l'espace triprojectif de tridegré (1,1,1). La constante obtenue dans le résultat final est celle conjecturée par Peyre. La méthode utilisée est celle développée par Schindler pour étudier le cas des hypersurfaces des espaces biprojectifs. Cette méthode est essentiellement basée sur la méthode du cercle de Hardy-Littlewood.

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Teddy Mignot. 2014-03-27. Points de hauteur bornée sur les hypersurfaces lisses de l'espace triprojectif. https://arxiv.org/abs/1403.6975

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