More cubic surfaces violating the Hasse principle

Jörg Jahnel[1]

  • [1] FB6 Mathematik Walter-Flex-Str. 3 D-57068 Siegen, Germany

Journal de Théorie des Nombres de Bordeaux (2011)

  • Volume: 23, Issue: 2, page 471-477
  • ISSN: 1246-7405

Abstract

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

How to cite

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Jahnel, Jörg. "More cubic surfaces violating the Hasse principle." Journal de Théorie des Nombres de Bordeaux 23.2 (2011): 471-477. <http://eudml.org/doc/219781>.

@article{Jahnel2011,
abstract = {We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.},
affiliation = {FB6 Mathematik Walter-Flex-Str. 3 D-57068 Siegen, Germany},
author = {Jahnel, Jörg},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {cubic surface; Hasse principle; counter-examples},
language = {eng},
month = {6},
number = {2},
pages = {471-477},
publisher = {Société Arithmétique de Bordeaux},
title = {More cubic surfaces violating the Hasse principle},
url = {http://eudml.org/doc/219781},
volume = {23},
year = {2011},
}

TY - JOUR
AU - Jahnel, Jörg
TI - More cubic surfaces violating the Hasse principle
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2011/6//
PB - Société Arithmétique de Bordeaux
VL - 23
IS - 2
SP - 471
EP - 477
AB - We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.
LA - eng
KW - cubic surface; Hasse principle; counter-examples
UR - http://eudml.org/doc/219781
ER -

References

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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. Zbl0277.14014MR833513
  3. L. J. Mordell, On the conjecture for the rational points on a cubic surface. J. London Math. Soc. 40 (1965), 149–158. Zbl0124.02605MR169815
  4. Sir Peter Swinnerton-Dyer, Two special cubic surfaces. Mathematika 9 (1962), 54–56. Zbl0103.38302MR139989
  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. Zbl1179.11041MR220697

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