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Varietes de descente, gerbes et obstruction de Brauer-Manin (Descent varieties, gerbes and Brauer-Manin obstruction)

Jean-Claude Douai·Michel Emsalem·Stephane Zahnd
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Abstract

Nous montrons comment associer à une gerbe définie sur un corps de nombres une obstruction de Brauer-Manin mesurant, comme dans le cas des variétés, le défaut d'existence d'une section globale. Ceci nous conduit à une généralisation de la dualité de Tate-Poitou au cas non-abélien. We find a way to associate to a gerbe defined over a number field a Brauer-Manin obstruction, which measures, as for varieties, the defect to the existence of a global section. This leads us to a generalization of Tate-Poitou duality in the non-abelian case.

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Jean-Claude Douai, Michel Emsalem, Stephane Zahnd. 2003-03-19. Varietes de descente, gerbes et obstruction de Brauer-Manin (Descent varieties, gerbes and Brauer-Manin obstruction). https://arxiv.org/abs/math/0303231

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