Geodesic
On Manin’s conjecture for a family of Châtelet surfaces
Régis de la Bretèche1 ; Tim Browning2 ; Emmanuel Peyre3
1 Institut de Mathématiques de Jussieu<br/> UMR 7586 Case 7012<br/> Université Paris 7 -- Denis Diderot<br/> 2, place Jussieu<br/> F-75251 Paris cedex 05<br/> France
2 School of Mathematics<br/> University of Bristol<br/> Bristol BS8 1TW<br/>England
3 Institut Fourier<br/> UMR 5582 du CNRS<br/> Université Joseph Fourier<br/> BP 74<br/> 38042 Saint-Martin d'Hères<br/> France
Annals of mathematics, Tome 175 (2012) no. 1, pp. 297-343.

Voir la notice de l'article provenant de la source Annals of Mathematics website

The Manin conjecture is established for Châtelet surfaces over $\mathbf{Q}$ arising as minimal proper smooth models of the surface $Y^2+Z^2=f(X)$ in $\mathbf{A}_{\mathbf{Q}}^3$, where $f\in \mathbf{Z}[X]$ is a totally reducible polynomial of degree $3$ without repeated roots. These surfaces do not satisfy weak approximation.
DOI : 10.4007/annals.2012.175.1.8

Régis de la Bretèche 1 ; Tim Browning 2 ; Emmanuel Peyre 3

1 Institut de Mathématiques de Jussieu<br/> UMR 7586 Case 7012<br/> Université Paris 7 -- Denis Diderot<br/> 2, place Jussieu<br/> F-75251 Paris cedex 05<br/> France
2 School of Mathematics<br/> University of Bristol<br/> Bristol BS8 1TW<br/>England
3 Institut Fourier<br/> UMR 5582 du CNRS<br/> Université Joseph Fourier<br/> BP 74<br/> 38042 Saint-Martin d'Hères<br/> France 
@article{10_4007_annals_2012_175_1_8,
     author = {R\'egis de la Bret\`eche and Tim Browning and Emmanuel Peyre},
     title = {On {Manin{\textquoteright}s} conjecture for a family of {Ch\^atelet} surfaces},
     journal = {Annals of mathematics},
     pages = {297--343},
     publisher = {mathdoc},
     volume = {175},
     number = {1},
     year = {2012},
     doi = {10.4007/annals.2012.175.1.8},
     mrnumber = {2874644},
     zbl = {06014077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.1.8/}
}
TY  - JOUR
AU  - Régis de la Bretèche
AU  - Tim Browning
AU  - Emmanuel Peyre
TI  - On Manin’s conjecture for a family of Châtelet surfaces
JO  - Annals of mathematics
PY  - 2012
SP  - 297
EP  - 343
VL  - 175
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.1.8/
DO  - 10.4007/annals.2012.175.1.8
LA  - en
ID  - 10_4007_annals_2012_175_1_8
ER  - 
%0 Journal Article
%A Régis de la Bretèche
%A Tim Browning
%A Emmanuel Peyre
%T On Manin’s conjecture for a family of Châtelet surfaces
%J Annals of mathematics
%D 2012
%P 297-343
%V 175
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.1.8/
%R 10.4007/annals.2012.175.1.8
%G en
%F 10_4007_annals_2012_175_1_8
Régis de la Bretèche; Tim Browning; Emmanuel Peyre. On Manin’s conjecture for a family of Châtelet surfaces. Annals of mathematics, Tome 175 (2012) no. 1, pp. 297-343. doi : 10.4007/annals.2012.175.1.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.1.8/

Cité par Sources :