Universal torsors and values of quadratic polynomials represented by norms

© 2014, Springer-Verlag Berlin Heidelberg. Let (Formula presented.) be an extension of number fields, and let (Formula presented.) be a quadratic polynomial over (Formula presented.). Let (Formula presented.) be the affine variety defined by (Formula presented.). We study the Hasse principle and weak approximation for (Formula presented.) in three cases. For (Formula presented.) and (Formula presented.) irreducible over (Formula presented.) and split in (Formula presented.), we prove the Hasse principle and weak approximation. For (Formula presented.) with arbitrary (Formula presented.), we show that the Brauer-Manin obstruction to the Hasse principle and weak approximation is the only one. For (Formula presented.) and (Formula presented.) irreducible over k, we determine the Brauer group of smooth proper models of X. In a case where it is non-trivial, we exhibit a counterexample to weak approximation.

Publication year:2015

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IOF-keylabel:yes

BOF-publication weight:2

CSS-citation score:2

Authors:International

Authors from:Higher Education

Accessibility:Open