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Descent obstruction is equivalent to étale Brauer–Manin obstruction

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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.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2BZ, UK

    Alexei Skorobogatov

  2. Russian Academy of Sciences, Institute for the Information Transmission Problems, 19 Bolshoi Karetnyi, 127994, Moscow, Russia

    Alexei Skorobogatov

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  1. Alexei Skorobogatov
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Correspondence to Alexei Skorobogatov.

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Skorobogatov, A. Descent obstruction is equivalent to étale Brauer–Manin obstruction. Math. Ann. 344, 501–510 (2009). https://doi.org/10.1007/s00208-008-0314-4

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  • DOI: https://doi.org/10.1007/s00208-008-0314-4

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