no. 6
The solubility of diagonal cubic surfaces
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 6, pp. 891-912. 
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     author = {Swinnerton-Dyer, Peter},
     title = {The solubility of diagonal cubic surfaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {891--912},
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     volume = {Ser. 4, 34},
     number = {6},
     year = {2001},
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     zbl = {1003.11028},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(01)01080-1/}
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Swinnerton-Dyer, Peter. The solubility of diagonal cubic surfaces. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 6, pp. 891-912. doi : 10.1016/s0012-9593(01)01080-1. http://archive.numdam.org/articles/10.1016/s0012-9593(01)01080-1/

[1] Bender A.O., Sir Swinnerton-Dyer P., Solubility of certain pencils of curves of genus 1, and of the intersection of two quadrics in P4, Proc. London Math. Soc. 83 (3) (2001) 299-329. | MR | Zbl

[2] Cassels J.W.S., Arithmetic on curves of genus 1, I. On a conjecture of Selmer, J. Reine Angew. Math. 202 (1959) 52-99. | MR | Zbl

[3] Cassels J.W.S., Guy M.J.T., On the Hasse principle for cubic surfaces, Mathematika 13 (1966) 111-120. | MR | Zbl

[4] Colliot-Thélène J.-L., Surfaces cubiques diagonales, in: Séminaire de théorie des nombres, Paris 1984-85, Progress in Math., 63, Birkhäuser, 1986, pp. 51-66. | MR | Zbl

[5] Colliot-Thélène J.-L., Kanevsky D., Sansuc J.-J., Arithmétique des surfaces cubiques diagonales, in: Diophantine Approximation and Transcendence Theory, Springer Lecture Notes, 1290, 1987, pp. 1-108. | MR | Zbl

[6] Colliot-Thélène J.-L., Skorobogatov A.N., Sir Swinnerton-Dyer P., Hasse principle for pencils of curves of genus one whose Jacobians have rational 2-division points, Invent. Math. 134 (1998) 579-650. | MR | Zbl

[7] Hasse H., Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, Jahresbericht der D.M.V. 35 (1926) 1-55. | JFM

[8] Heath-Brown D.R., The solubility of diagonal cubic diophantine equations, Proc. London Math. Soc. (3) 79 (1999) 241-259. | MR | Zbl

[9] Kanevsky D., Application of the conjecture on the Manin obstruction to various Diophantine problems, Astérisque 147-148 (1987) 307-314. | Numdam | MR | Zbl

[10] Milne J.S., Arithmetic Duality Theorems, Academic Press, 1986. | MR | Zbl

[11] Selmer E.S., Sufficient congruence conditions for the existence of rational points on certain cubic surfaces, Math. Scand. 1 (1953) 113-119. | EuDML | MR | Zbl

[12] Sir Swinnerton-Dyer P., Some applications of Schinzel's Hypothesis to Diophantine Equations, in: Györy , Iwaniec , Urbanowicz (Eds.), Number Theory in Progress, 1999. | Zbl

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