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Time: Friday, April 13, 2012, 14h30-15h30

Location: salle W

Universal torsors and values of quadratic polynomials represented by norms

Dasheng Wei (Pekin / Munich - Personal website)

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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