Publications at the Riemann Center

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)
Universität Paris-Süd
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
Mathematik (insg.)
Electronic version(s)
https://doi.org/10.1007/s00208-014-1106-7 (Access: Unbekannt)