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Mathematische Annalen

, Volume 344, Issue 3, pp 501–510 | Cite as

Descent obstruction is equivalent to étale Brauer–Manin obstruction

  • Alexei SkorobogatovEmail author
Article

Abstract

Let X be a projective variety over a number field. Completing earlier work of D. Harari, C. Demarche and M. Stoll, we prove that the obstruction to the Hasse principle and weak approximation on X given by descent on torsors under linear algebraic groups is equivalent to the Brauer–Manin obstruction applied to étale covers of X.

Keywords

Smooth Projective Variety Weak Approximation Abelian Surface Kodaira Dimension Enriques Surface 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Russian Academy of SciencesInstitute for the Information Transmission ProblemsMoscowRussia

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