Universal torsors and values of quadratic polynomials represented by norms

Details Universal torsors and values of quadratic polynomials represented by norms Universal torsors and values of quadratic polynomials represented by norms

2012-02-16

arxiv.org/abs/1202.3567v1

Mathematics

Number Theory

12 pages

Scientific paper

Let K/k be an extension of number fields, and let P(t) be a quadratic polynomial over k. Let X be the affine variety defined by P(t) = N_{K/k}(z). We study the Hasse principle and weak approximation for X in two cases. For [K:k]=4 and P(t) irreducible over k and split in K, we prove the Hasse principle and weak approximation. For k=Q with arbitrary K, we show that the Brauer-Manin obstruction to the Hasse principle and weak approximation is the only one.

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