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Bianca Viray
Failure of the Hasse principle for Châtelet surfaces in characteristic $2$
Journal de théorie des nombres de Bordeaux, 24 no. 1 (2012), p. 231-236, doi: 10.5802/jtnb.794
Article PDF | Reviews MR 2914907 | Zbl pre06075028
Class. Math.: 11G35, 14G05, 14G25, 14G40
Keywords: Hasse principle, Brauer-Manin obstruction, Châtelet surface, rational points

Résumé - 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.

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