Failure of the Hasse principle for Châtelet surfaces in characteristic

Bianca Viray[1]

  • [1] Mathematics Department Box 1917 Brown University Providence, RI 02912 USA

Journal de Théorie des Nombres de Bordeaux (2012)

  • Volume: 24, Issue: 1, page 231-236
  • ISSN: 1246-7405

Abstract

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Given any global field of characteristic , we construct a Châtelet surface over that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic , thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.

How to cite

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Viray, Bianca. "Failure of the Hasse principle for Châtelet surfaces in characteristic $2$." Journal de Théorie des Nombres de Bordeaux 24.1 (2012): 231-236. <http://eudml.org/doc/251096>.

@article{Viray2012,
abstract = {Given any global field $k$ of characteristic $2$, we construct a Châtelet surface over $k$ that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic $2$, thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.},
affiliation = {Mathematics Department Box 1917 Brown University Providence, RI 02912 USA},
author = {Viray, Bianca},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Hasse principle; Brauer-Manin obstruction; Châtelet surface; rational points},
language = {eng},
month = {3},
number = {1},
pages = {231-236},
publisher = {Société Arithmétique de Bordeaux},
title = {Failure of the Hasse principle for Châtelet surfaces in characteristic $2$},
url = {http://eudml.org/doc/251096},
volume = {24},
year = {2012},
}

TY - JOUR
AU - Viray, Bianca
TI - Failure of the Hasse principle for Châtelet surfaces in characteristic $2$
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2012/3//
PB - Société Arithmétique de Bordeaux
VL - 24
IS - 1
SP - 231
EP - 236
AB - Given any global field $k$ of characteristic $2$, we construct a Châtelet surface over $k$ that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic $2$, thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.
LA - eng
KW - Hasse principle; Brauer-Manin obstruction; Châtelet surface; rational points
UR - http://eudml.org/doc/251096
ER -

References

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  5. Bjorn Poonen, Existence of rational points on smooth projective varieties. J. Eur. Math. Soc. (JEMS) 11 (2009), no. 3, 529–543. Zbl1183.14032MR2505440
  6. Bjorn Poonen, Insufficiency of the Brauer-Manin obstruction applied to étale covers. Ann. of Math. (2) 171 (2010), no. 3, 2157–2169. Zbl1284.11096MR2680407
  7. Jean-Pierre Serre, Local fields. Graduate Texts in Mathematics, vol. 67, Translated from the French by Marvin Jay Greenberg, Springer-Verlag, New York, 1979. Zbl0423.12016MR554237
  8. Alexei Skorobogatov, Torsors and rational points. Cambridge Tracts in Mathematics, vol. 144, Cambridge University Press, Cambridge, 2001. Zbl0972.14015MR1845760

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