Failure of the Hasse principle for Châtelet surfaces in characteristic 2
Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 1, pp. 231-236.

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.

Soit k un corps global de caractéristique 2. On construit une surface de Châtelet sur k possédant une obstruction de Brauer-Manin au principe de Hasse. Cette construction étend un résultat de Poonen à la caractéristique 2, en montrant ainsi que l’obstruction de Brauer-Manin après revêtement fini étale n’est pas suffisante pour expliquer tous les contre-exemples au principe de Hasse sur un corps global arbitraire.

Received:
Revised:
Published online:
DOI: 10.5802/jtnb.794
Classification: 11G35,  14G05,  14G25,  14G40
Keywords: Hasse principle, Brauer-Manin obstruction, Châtelet surface, rational points
Bianca Viray 1

1 Mathematics Department Box 1917 Brown University Providence, RI 02912 USA
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Bianca Viray. Failure of the Hasse principle for Châtelet surfaces in characteristic $2$. Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 1, pp. 231-236. doi : 10.5802/jtnb.794. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.794/

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