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Local-global principle for certain biquadratic normic bundles

Volume 164 / 2014

Yang Cao, Yongqi Liang Acta Arithmetica 164 (2014), 137-144 MSC: Primary 11G35; Secondary 14G25, 14G05, 14D10, 14C25. DOI: 10.4064/aa164-2-3

Abstract

Let $X$ be a proper smooth variety having an affine open subset defined by the normic equation $N_{k(\sqrt {a},\sqrt {b})/k}({\textbf {x}})=Q(t_{1},\ldots ,t_{m})^{2}$ over a number field $k$. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of $X;$ (2) the analogue for rational points is also valid assuming Schinzel's hypothesis.

Authors

  • Yang CaoSchool of Mathematical Sciences
    Capital Normal University
    105 Xisanhuanbeilu
    100048 Beijing, China
    e-mail
  • Yongqi LiangInstitut de Mathématiques de Jussieu
    – Paris Rive Gauche
    Université Paris Diderot – Paris 7
    Bâtiment Sophie Germain
    75013 Paris, France
    e-mail

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