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arXiv · 1411.7249

Points de hauteur born\'ee sur les hypersurfaces lisses des vari\'et\'es toriques

Teddy Mignot
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Abstract

We demonstrate the Batyrev-Manin Conjecture for the number of points of bounded height on hypersurfaces of some toric varieties whose rank of the Picard group is 2. The method used is inspired by the one developed by Schindler for the study the case of hypersurfaces of biprojective spaces. This method is based on the Hardy-Littlewood circle method. The constant obtained in the final asymptotic formula is the one conjectured by Peyre. ----- Nous d\'emontrons la conjecture de Batyrev-Manin pour le nombre de points de hauteur born\'ee sur les hypersurfaces de certaines vari\'et\'es toriques dont le rang du groupe de Picard est 2. La m\'ethode utilis\'ee est inspir\'ee de celle d\'evelopp\'ee par Schindler pour l'\'etude du cas des hypersurfaces des espaces biprojectifs. Cette m\'ethode est bas\'ee sur la m\'ethode du cercle de Hardy-Littlewood. La constante obtenue dans la formule asymptotique finale est celle conjectur\'ee par Peyre.

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Teddy Mignot. 2014-11-26. Points de hauteur born\'ee sur les hypersurfaces lisses des vari\'et\'es toriques. https://arxiv.org/abs/1411.7249

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