On Manin's conjecture for a family of Châtelet surfaces

article On Manin's conjecture for a family of Châtelet surfaces published Régis De La Bretèche author Timothy D Browning author 35827D50-F248-11E8-B48F-1D18A9856A870000-0002-8314-0177 Emmanuel Peyre author 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. Princeton University Press2012 Annals of Mathematics10.4007/annals.2012.175.1.8 1751297 - 343 yes R. De La Bretèche, T.D. Browning, E. Peyre, Annals of Mathematics 175 (2012) 297–343. 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:<a href="https://doi.org/10.4007/annals.2012.175.1.8">10.4007/annals.2012.175.1.8</a>. 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. Princeton University Press, pp. 297–343, 2012. De La Bretèche, R., Browning, T. D., & Peyre, E. (2012). On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics. Princeton University Press. <a href="https://doi.org/10.4007/annals.2012.175.1.8">https://doi.org/10.4007/annals.2012.175.1.8</a> 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:<a href="https://doi.org/10.4007/annals.2012.175.1.8">10.4007/annals.2012.175.1.8</a> De La Bretèche, Régis, Timothy D Browning, and Emmanuel Peyre. “On Manin’s Conjecture for a Family of Châtelet Surfaces.” Annals of Mathematics. Princeton University Press, 2012. <a href="https://doi.org/10.4007/annals.2012.175.1.8">https://doi.org/10.4007/annals.2012.175.1.8</a>. 2372018-12-11T11:45:22Z2021-01-12T06:57:04Z