Rational points on pencils of conics and quadrics with many degenerate fibres

T. D. Browning*, L. Matthiesen, A. N. Skorobogatov

*Corresponding author for this work

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

17 Citations (Scopus)
36 Downloads (Pure)

Abstract

For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.

Original languageEnglish
Pages (from-to)381-402
Number of pages22
JournalAnnals of Mathematics
Volume180
Issue number1
DOIs
Publication statusPublished - 1 Jul 2014

Keywords

  • BINARY QUADRATIC-FORMS
  • HASSE PRINCIPLE
  • WEAK APPROXIMATION
  • PROJECTIVE LINE
  • DESCENT
  • SURFACES
  • FIBRATIONS
  • VARIETIES
  • BUNDLES

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