Geodesic
Local-global principle for certain biquadratic normic bundles
Yang Cao 1   ; Yongqi Liang 2
1 School of Mathematical Sciences Capital Normal University 105 Xisanhuanbeilu 100048 Beijing, China
2 Institut de Mathématiques de Jussieu – Paris Rive Gauche Université Paris Diderot – Paris 7 Bâtiment Sophie Germain 75013 Paris, France
Acta Arithmetica, Tome 164 (2014) no. 2, pp. 137-144 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa164-2-3
Keywords: proper smooth variety having affine subset defined normic equation sqrt sqrt textbf ldots number field nbsp prove failure local global principle zero cycles controlled brauer group analogue rational points valid assuming schinzels hypothesis

Yang Cao  1   ; Yongqi Liang  2

1 School of Mathematical Sciences Capital Normal University 105 Xisanhuanbeilu 100048 Beijing, China
2 Institut de Mathématiques de Jussieu – Paris Rive Gauche Université Paris Diderot – Paris 7 Bâtiment Sophie Germain 75013 Paris, France 
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Yang Cao; Yongqi Liang. Local-global principle for certain biquadratic normic bundles. Acta Arithmetica, Tome 164 (2014) no. 2, pp. 137-144. doi: 10.4064/aa164-2-3

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