Geodesic
Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques
Teddy Mignot1
1 Institut Fourier, UMR 5582 UFR de Mathématiques, Université de Grenoble I BP 74, 38402 Saint-Martin d’Hères Cedex, France
Acta Arithmetica, Tome 172 (2016) no. 1, pp. 1-97.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 case of hypersurfaces of biprojective spaces and by Blomer and Brüdern for some hypersurfaces of multiprojective spaces. These methods are based on the Hardy–Littlewood circle method. The constant obtained in the final asymptotic formula is the one conjectured by Peyre.
DOI : 10.4064/aa8050-12-2015
Mots-clés : demonstrate batyrev manin conjecture number points bounded height hypersurfaces toric varieties whose rank picard group method inspired developed schindler hypersurfaces biprojective spaces blomer dern hypersurfaces multiprojective spaces these methods based hardy littlewood circle method constant obtained final asymptotic formula conjectured peyre

Teddy Mignot 1

1 Institut Fourier, UMR 5582 UFR de Mathématiques, Université de Grenoble I BP 74, 38402 Saint-Martin d’Hères Cedex, France 
@article{10_4064_aa8050_12_2015,
     author = {Teddy Mignot},
     title = {Points de hauteur born\'ee sur les hypersurfaces lisses des vari\'et\'es toriques},
     journal = {Acta Arithmetica},
     pages = {1--97},
     publisher = {mathdoc},
     volume = {172},
     number = {1},
     year = {2016},
     doi = {10.4064/aa8050-12-2015},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8050-12-2015/}
}
TY  - JOUR
AU  - Teddy Mignot
TI  - Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques
JO  - Acta Arithmetica
PY  - 2016
SP  - 1
EP  - 97
VL  - 172
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8050-12-2015/
DO  - 10.4064/aa8050-12-2015
LA  - fr
ID  - 10_4064_aa8050_12_2015
ER  - 
%0 Journal Article
%A Teddy Mignot
%T Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques
%J Acta Arithmetica
%D 2016
%P 1-97
%V 172
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8050-12-2015/
%R 10.4064/aa8050-12-2015
%G fr
%F 10_4064_aa8050_12_2015
Teddy Mignot. Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques. Acta Arithmetica, Tome 172 (2016) no. 1, pp. 1-97. doi : 10.4064/aa8050-12-2015. http://geodesic.mathdoc.fr/articles/10.4064/aa8050-12-2015/

Cité par Sources :