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

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

2003-03-19

arxiv.org/abs/math/0303231v1

Mathematics

Number Theory

14 pages, uses xypic

Scientific paper

Nous montrons comment associer \`a une gerbe d\'efinie sur un corps de nombres une obstruction de Brauer-Manin mesurant, comme dans le cas des vari\'et\'es, le d\'efaut d'existence d'une section globale. Ceci nous conduit \`a une g\'en\'eralisation de la dualit\'e de Tate-Poitou au cas non-ab\'elien. 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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