Norm forms for arbitrary number fields as products of linear polynomials

Tim D Browning, Lilian Matthiesen

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
239 Downloads (Pure)

Abstract

Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the variety defined by the equation NK (x) = P (t). Combining additive combinatiorics with descent we show that the Brauer-Manin obstruction is the only obstruction to the Hesse principle and weak approximation on any smooth and projective model of X.
Original languageEnglish
Pages (from-to)1383-1446
Number of pages64
JournalAnnales Scientifiques de l'École Normale Supérieure
Volume50
Issue number6
Early online date24 Nov 2017
DOIs
Publication statusPublished - Nov 2017

Keywords

  • additive combinatorics
  • Brauer-Manin obstruction
  • descent
  • Hasse principle
  • norm forms
  • weak approximation

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