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Sous-groupe de Brauer
invariant et obstruction de descente itérée
Yang Cao |
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Vol. 14 (2020), No. 8, 2151–2183
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DOI: 10.2140/ant.2020.14.2151
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Abstract |
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Pour une variété quasi-projective, lisse, géométriquement intègre sur un corps de nombres , on montre que l’obstruction de descente itérée est équivalente à l’obstruction de descente. Ceci généralise un résultat de Skorobogatov, et ceci répond à une question ouverte de Poonen. Les outils principaux sont la notion de sous-groupe de Brauer invariant et la notion d’obstruction de Brauer–Manin étale invariante pour une -variété munie d’une action d’un groupe linéaire connexe. For a quasi-projective smooth geometrically integral variety over a number field , 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. Our main tools are the notion of invariant Brauer subgroup and the notion of invariant étale Brauer–Manin obstruction for a -variety equipped with an action of a connected linear algebraic group. |
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Keywords
Hasse principle, Brauer–Manin obstruction, algebraic group
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Mathematical Subject Classification 2010
Primary: 11G35
Secondary: 14G05, 20G35
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Milestones
Received: 23 July 2019
Revised: 10 February 2020
Accepted: 12 April 2020
Published: 18 September 2020
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Authors |
| Yang Cao | |
| IAZD, Leibniz Universität
Hannover Germany |
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