More cubic surfaces violating the Hasse principle
Jörg Jahnel1
1 FB6 Mathematik Walter-Flex-Str. 3 D-57068 Siegen, Germany
Journal de théorie des nombres de Bordeaux, Volume 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.

DOI: 10.5802/jtnb.772
Jörg Jahnel 1

1 FB6 Mathematik Walter-Flex-Str. 3 D-57068 Siegen, Germany 
@article{JTNB_2011__23_2_471_0,
     author = {J\"org Jahnel},
     title = {More cubic surfaces violating the {Hasse} principle},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {471--477},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {23},
     number = {2},
     year = {2011},
     doi = {10.5802/jtnb.772},
     mrnumber = {2817940},
     zbl = {1233.11033},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.772/}
}
TY  - JOUR
AU  - Jörg Jahnel
TI  - More cubic surfaces violating the Hasse principle
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2011
SP  - 471
EP  - 477
VL  - 23
IS  - 2
PB  - Société Arithmétique de Bordeaux
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.772/
DO  - 10.5802/jtnb.772
LA  - en
ID  - JTNB_2011__23_2_471_0
ER  - 
%0 Journal Article
%A Jörg Jahnel
%T More cubic surfaces violating the Hasse principle
%J Journal de théorie des nombres de Bordeaux
%D 2011
%P 471-477
%V 23
%N 2
%I Société Arithmétique de Bordeaux
%U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.772/
%R 10.5802/jtnb.772
%G en
%F JTNB_2011__23_2_471_0
Jörg Jahnel. More cubic surfaces violating the Hasse principle. Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 2, pp. 471-477. doi : 10.5802/jtnb.772. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.772/

[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

Cited by Sources: