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arXiv · 1704.05425

Sous-groupe de Brauer invariant et obstruction de descente itérée

Yang Cao
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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.

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BibTeXRIS

Yang Cao. 2020-03-19. Sous-groupe de Brauer invariant et obstruction de descente itérée. https://doi.org/10.2140/ant.2020.14.2151

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