Soit un corps global de caractéristique . On construit une surface de Châtelet sur possédant une obstruction de Brauer-Manin au principe de Hasse. Cette construction étend un résultat de Poonen à la caractéristique , 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.
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.
Mots clés : Hasse principle, Brauer-Manin obstruction, Châtelet surface, rational points
@article{JTNB_2012__24_1_231_0,
author = {Viray, Bianca},
title = {Failure of the {Hasse} principle for {Ch\^atelet} surfaces in characteristic $2$},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {231--236},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {24},
number = {1},
year = {2012},
doi = {10.5802/jtnb.794},
mrnumber = {2914907},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/jtnb.794/}
}
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 PY - 2012 SP - 231 EP - 236 VL - 24 IS - 1 PB - Société Arithmétique de Bordeaux UR - http://archive.numdam.org/articles/10.5802/jtnb.794/ DO - 10.5802/jtnb.794 LA - en ID - JTNB_2012__24_1_231_0 ER -
%0 Journal Article %A Viray, Bianca %T Failure of the Hasse principle for Châtelet surfaces in characteristic $2$ %J Journal de théorie des nombres de Bordeaux %D 2012 %P 231-236 %V 24 %N 1 %I Société Arithmétique de Bordeaux %U http://archive.numdam.org/articles/10.5802/jtnb.794/ %R 10.5802/jtnb.794 %G en %F JTNB_2012__24_1_231_0
Viray, Bianca. Failure of the Hasse principle for Châtelet surfaces in characteristic $2$. Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 1, pp. 231-236. doi : 10.5802/jtnb.794. http://archive.numdam.org/articles/10.5802/jtnb.794/
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