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arXiv · 1303.5221

Le groupe de Brauer non ramifi\'e sur un corps global de caract\'eristique positive (The unramified Brauer group over a global field of positive characteristic)

Giancarlo Lucchini Arteche
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Abstract

En utilisant un th\'eor\`eme de Gabber sur les alt\'erations, on d\'emontre un r\'esultat d\'ecrivant la partie de torsion premi\`ere \`a $p$ du groupe de Brauer non ramifi\'e d'une vari\'et\'e $V$ lisse et g\'eom\'etriquement int\`egre sur un corps global de caract\'eristique $p$ au moyen de l'\'evaluation des \'el\'ements de $\Br V$ sur ses points locaux. Using a theorem of Gabber on alterations, we prove a result describing the prime-to-$p$ torsion part of the unramified Brauer group of a smooth and geometrically integral variety $V$ over a global field of characteristic $p$ by evaluating the elements of $\Br V$ at its local points.

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Giancarlo Lucchini Arteche. 2013-03-21. Le groupe de Brauer non ramifi\'e sur un corps global de caract\'eristique positive (The unramified Brauer group over a global field of positive characteristic). https://doi.org/10.1016/j.crma.2013.04.020

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