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Norm forms for arbitrary number fields as products of linear polynomials

Research output: Contribution to journalArticle

  • Tim D Browning
  • Lilian Matthiesen
Original languageEnglish
Pages (from-to)1375-1438
Number of pages63
JournalAnnales Scientifiques de l'École Normale Supérieure
Volume50
Issue number6
Early online date24 Nov 2017
DOIs
DateAccepted/In press - 31 Aug 2016
DateE-pub ahead of print - 24 Nov 2017
DatePublished (current) - Nov 2017

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.

    Research areas

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

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Societe Mathematique de France at http://smf4.emath.fr/Publications/AnnalesENS/4_50/html/ens_ann-sc_50_1383-1446.php . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 673 KB, PDF document

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