On Manin's conjecture for a family of Châtelet surfaces

R. De La Bretèche, T.D. Browning, E. Peyre, Annals of Mathematics 175 (2012) 297–343.

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Abstract
The Manin conjecture is established for Châtelet surfaces over Q aris-ing as minimal proper smooth models of the surface Y 2 + Z 2 = f(X) in A 3 Q, where f ∈ Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation.
Publishing Year
Date Published
2012-01-01
Journal Title
Annals of Mathematics
Acknowledgement
EP/E053262/1 Engineering and Physical Sciences Research Council
Volume
175
Issue
1
Page
297 - 343
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De La Bretèche R, Browning TD, Peyre E. On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics. 2012;175(1):297-343. doi:10.4007/annals.2012.175.1.8
De La Bretèche, R., Browning, T. D., & Peyre, E. (2012). On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics, 175(1), 297–343. https://doi.org/10.4007/annals.2012.175.1.8
De La Bretèche, Régis, Timothy D Browning, and Emmanuel Peyre. “On Manin’s Conjecture for a Family of Châtelet Surfaces.” Annals of Mathematics 175, no. 1 (2012): 297–343. https://doi.org/10.4007/annals.2012.175.1.8.
R. De La Bretèche, T. D. Browning, and E. Peyre, “On Manin’s conjecture for a family of Châtelet surfaces,” Annals of Mathematics, vol. 175, no. 1, pp. 297–343, 2012.
De La Bretèche R, Browning TD, Peyre E. 2012. On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics. 175(1), 297–343.
De La Bretèche, Régis, et al. “On Manin’s Conjecture for a Family of Châtelet Surfaces.” Annals of Mathematics, vol. 175, no. 1, Princeton University Press, 2012, pp. 297–343, doi:10.4007/annals.2012.175.1.8.

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