Comparing descent obstruction and Brauer-Manin obstruction for open varieties
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- by Yang Cao, Cyril Demarche and Fei Xu PDF
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Abstract:
We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over not necessarily proper varieties under a connected linear algebraic group or a group of multiplicative type. Such a relation is also refined for torsors under a torus. The equivalence between descent obstruction and étale Brauer-Manin obstruction for smooth projective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points.References
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Additional Information
- Yang Cao
- Affiliation: Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
- Address at time of publication: Department of Mathematics and Physics, Leibniz University Hannover, Germany
- MR Author ID: 1070471
- Email: yangcao1988@gmail.com
- Cyril Demarche
- Affiliation: Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Université Paris Diderot, Sorbonne Paris Cité, F-75005, Paris, France – and – Département de mathématiques et applications, École normale supérieure, 45 rue d’Ulm, 75230 Paris Cedex 05, France
- MR Author ID: 867113
- Email: cyril.demarche@imj-prg.fr
- Fei Xu
- Affiliation: School of Mathematical Sciences, Capital Normal University, 105 Xisanhuanbeilu, 100048 Beijing, People’s Republic of China
- Email: xufei@math.ac.cn
- Received by editor(s): November 18, 2016
- Received by editor(s) in revised form: July 29, 2017, and November 28, 2017
- Published electronically: March 7, 2019
- Additional Notes: The first named author acknowledges the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-12-BL01-0005.
The second named author acknowledges the support of the French Agence Nationale de la Recherche (ANR) under references ANR-12-BL01-0005 and ANR-15-CE40-0002-01.
The third named author acknowledges the support of NSFC grants no. 11471219 and 11631009. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 8625-8650
- MSC (2010): Primary 14G05
- DOI: https://doi.org/10.1090/tran/7567
- MathSciNet review: 3955558