More cubic surfaces violating the Hasse principle
Jörg Jahnel1
1FB6 Mathematik Walter-Flex-Str. 3 D-57068 Siegen, Germany
Journal de théorie des nombres de Bordeaux, Tome 23 (2011) no. 2, pp. 471-477

We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.

Nous généralisons la construction due à L. J. Mordell de surfaces cubiques pour lesquelles le principe de Hasse est faux.

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DOI : 10.5802/jtnb.772

Jörg Jahnel  1

1 FB6 Mathematik Walter-Flex-Str. 3 D-57068 Siegen, Germany 
Jörg Jahnel. More cubic surfaces violating the Hasse principle. Journal de théorie des nombres de Bordeaux, Tome 23 (2011) no. 2, pp. 471-477. doi: 10.5802/jtnb.772
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[1] J. Jahnel, Brauer groups, Tamagawa measures, and rational points on algebraic varieties. Habilitation thesis, Göttingen, 2008.

[2] Yu. I. Manin, Cubic forms, algebra, geometry, arithmetic. North-Holland Publishing Co. and American Elsevier Publishing Co., Amsterdam-London and New York, 1974. | MR | Zbl

[3] L. J. Mordell, On the conjecture for the rational points on a cubic surface. J. London Math. Soc. 40 (1965), 149–158. | MR | Zbl

[4] Sir Peter Swinnerton-Dyer, Two special cubic surfaces. Mathematika 9 (1962), 54–56. | MR | Zbl

[5] J. Tate, Global class field theory. In: Algebraic number theory, Edited by J. W. S. Cassels and A. Fröhlich, Academic Press and Thompson Book Co., London and Washington, 1967. | MR | Zbl

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