Weak approximation for cubic hypersurfaces of large dimension

Michael P Swarbrick Jones

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

2 Citations (Scopus)

Abstract

We address the problem of weak approximation for general cubic hypersurfaces defined over number fields with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically integral, nonconical cubic hypersurfaces of dimension at least 17. The proof utilises the Hardy-Littlewood circle method and the fibration method.

Original languageEnglish
Pages (from-to)1353-1363
Number of pages11
JournalAlgebra and Number Theory
Volume7
Issue number6
DOIs
Publication statusPublished - 2013

Keywords

  • cubic hypersurfaces
  • weak approximation
  • local-global principles
  • fibration method
  • circle method
  • many variables
  • NUMBER-FIELDS
  • SURFACES

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