Sous-groupe de Brauer invariant et obstruction de descente itérée

Abstract

For a quasi-projective smooth geometrically integral variety over a number field $k$, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a result of Skorobogatov, and this answers an open question of Poonen. The key idea is the notion of invariant Brauer subgroup and the notion of invariant étale Brauer-Manin obstruction for a $k$-variety equipped with an action of a connected linear algebraic group.

in French, 30 pages

References in corpus (1)

• Approximation forte pour les variétés avec une action d'un groupe linéaire

Cited by in corpus (3)

• A note on the Brauer group and the Brauer-Manin set of a product
• Boundedness of the p-primary torsion of the Brauer group of products of varieties
• Corrigendum à "Sous-groupe de Brauer invariant et obstruction de descente itérée" Algebra & Number Theory 14 (2020), no. 8, 2151--2183