On the order three Brauer classes for cubic surfaces

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1. [1] Buckley A., Košir T., Determinantal representations of smooth cubic surfaces, Geom. Dedicata, 2007, 125, 115–140 http://dx.doi.org/10.1007/s10711-007-9144-x Zbl1117.14038
2. [2] Cartan H., Eilenberg S., Homological Algebra, Princeton University Press, Princeton, 1956 
3. [3] Cassels J.W.S., Guy M.J.T., On the Hasse principle for cubic surfaces, Mathematika, 1966, 13, 111–120 http://dx.doi.org/10.1112/S0025579300003879 Zbl0151.03405
4. [4] Clebsch A., Die Geometrie auf den Flächen dritter Ordnung, J. Reine Angew. Math., 1866, 1866(65), 359–380 http://dx.doi.org/10.1515/crll.1866.65.359 
5. [5] Colliot-Thélène J.-L., Kanevsky D., Sansuc J.-J., Arithmétique des surfaces cubiques diagonales, In: Diophantine Approximation and Transcendence Theory, Bonn, May–June, 1985, Lecture Notes in Math., 1290, Springer, Berlin, 1987, 1–108 http://dx.doi.org/10.1007/BFb0078705 
6. [6] Cremona L., Sulle ventisette rette della superficie del terzo ordine, Istit. Lombardo Accad. Sci. Lett. Rend. A, 1870, 3, 209–219 
7. [7] Dolgachev I.V., Classical Algebraic Geometry, Cambridge University Press (in press), available at http://www.math.lsa.umich.edu/_idolga/CAG.pdf Zbl1252.14001
8. [8] Elsenhans A.-S., Jahnel J., Experiments with general cubic surfaces, In: Algebra, Arithmetic, and Geometry: in Honor of Yu.I. Manin, 1, Progr. Math., 269, Birkhäuser, Boston, 2007, 637–653 
9. [9] Elsenhans A.-S., Jahnel J., On the Brauer-Manin obstruction for cubic surfaces, J. Comb. Number Theory, 2010, 2(2), 107–128 Zbl1245.14020
10. [10] Elsenhans A.-S., Jahnel J., Cubic surfaces with a Galois invariant pair of Steiner trihedra, Int. J. Number Theory, 2011, 7(4), 947–970 http://dx.doi.org/10.1142/S1793042111004253 Zbl1233.11073
11. [11] Elsenhans A.-S., Jahnel J., On the quasi group of a cubic surface over a finite field, J. Number Theory (in press) 
12. [12] Hartshorne R., Algebraic Geometry, Grad. Texts in Math., 52, Springer, New York-Heidelberg, 1977 
13. [13] Henderson A., The Twenty-Seven Lines upon the Cubic Surface, Hafner, New York, 1960 Zbl42.0661.01
14. [14] Jahnel J., More cubic surfaces violating the Hasse principle, J. Théor. Nombres Bordeaux, 2011, 23(2), 471–477 http://dx.doi.org/10.5802/jtnb.772 Zbl1233.11033
15. [15] Kresch A., Tschinkel Yu., On the arithmetic of del Pezzo surfaces of degree 2, Proc. London Math. Soc., 2004, 89(3), 545–569 http://dx.doi.org/10.1112/S002461150401490X Zbl1075.14019
16. [16] Kunyavskiĭ B.È., Skorobogatov A.N., Tsfasman M.A., Del Pezzo Surfaces of Degree Four, Mém. Soc. Math. France (N.S.), 37, Société Mathématique de France, Marseille, 1989 Zbl0705.14039
17. [17] Manin Yu.I., Cubic Forms: Algebra, Geometry, Arithmetic, North-Holland Math. Library, 4, North-Holland/Elsevier, Amsterdam-London/New York, 1974 
18. [18] Mordell L.J., On the conjecture for the rational points on a cubic surface, J. London Math. Soc., 1965, 40, 149–158 http://dx.doi.org/10.1112/jlms/s1-40.1.149 Zbl0124.02605
19. [19] Neukirch J., Klassenkörpertheorie, 2nd ed., Springer-Lehrbuch, Springer, Berlin, 2011 http://dx.doi.org/10.1007/978-3-642-17325-7 
20. [20] Peyre E., Hauteurs et mesures de Tamagawa sur les variétés de Fano, Duke Math. J., 1995, 79(1), 101–218 http://dx.doi.org/10.1215/S0012-7094-95-07904-6 
21. [21] Peyre E., Tschinkel Yu., Tamagawa numbers of diagonal cubic surfaces, numerical evidence, Math. Comp., 2001, 70(233), 367–387 http://dx.doi.org/10.1090/S0025-5718-00-01189-3 Zbl0961.14012
22. [22] Schläfli L., An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface, The Quarterly Journal of Pure and Applied Mathematics, 1858, 2, 110–120 
23. [23] Serre J.-P., Local class field theory, In: Algebraic Number Theory, Brighton, 1965, Thompson, Washington, 1967, 128–161 
24. [24] Steiner J., Über die Flächen dritten Grades, J. Reine Angew. Math., 1857, 53, 133–141 http://dx.doi.org/10.1515/crll.1857.53.133 
25. [25] Swinnerton-Dyer H.P.F., Two special cubic surfaces, Mathematika, 1962, 9, 54–56 http://dx.doi.org/10.1112/S0025579300003090 Zbl0103.38302
26. [26] Swinnerton-Dyer H.P.F., Universal equivalence for cubic surfaces over finite and local fields, In: Symposia Mathematica, 24, Rome, April 9–14, 1979, Academic Press, London-New York, 1981, 111–143 
27. [27] Swinnerton-Dyer P., The Brauer group of cubic surfaces, Math. Proc. Cambridge Philos. Soc., 1993, 113(3), 449–460 http://dx.doi.org/10.1017/S0305004100076106 Zbl0804.14018
28. [28] Tate J.T., Global class field theory, In: Algebraic Number Theory, Brighton, 1965, Thompson, Washington, 1967, 162–203 Zbl1179.11041