Universal torsors and values of quadratic polynomials represented by norms

authored by

Ulrich Derenthal, Arne Smeets, Dasheng Wei

Abstract

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.

Organisation(s)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Riemann Center for Geometry and Physics

External Organisation(s)

KU Leuven
Chinese Academy of Sciences (CAS)
Université Paris XI

Type

Artikel

Journal

Mathematische Annalen

Volume

361

Pages

1021-1042

No. of pages

22

ISSN

0025-5831

Publication date

04.2015

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Allgemeine Mathematik

Electronic version(s)

https://doi.org/10.1007/s00208-014-1106-7 (Access: Unbekannt)