Weak Approximation on Del Pezzo Surfaces of Degree 4

  • Peter Swinnerton-Dyer
Part of the Progress in Mathematics book series (PM, volume 226)


Let V be a Del Pezzo surface of degree 4 over a number field k such that V(k) ≠ ø. We prove that V(k) = V(A)Br.


Local Solubility Algebraic Number Field Ideal Class Group Singular Fibre Hilbert Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J.-L. Colliot-Thélène & P. Swinnerton-Dyer — Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties, J. Reine Angew. Math. 453 (1994), 49–112.MATHMathSciNetGoogle Scholar
  2. [2]
    P. Salberger & A. N. Skorobogatov — Weak approximation for surfaces defined by two quadratic forms, Duke Math. J. 63 (1991), no. 2, 517–536.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    P. Swinnerton-Dyer — Rational points on pencils of conics and on pencils of quadrics, J. London Math. Soc. (2)50 (1994), no. 2, 231–242.MathSciNetCrossRefGoogle Scholar
  4. [4]
    P. Swinnerton-Dyer, Some applications of Schinzel’s hypothesis to Diophantine equations, Number theory in progress, Vol. 1 (Zakopane-Koscielisko, 1997), de Gruyter, Berlin, 1999, 503–530.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Peter Swinnerton-Dyer
    • 1
  1. 1.DPMMS, Centre for Mathematical Sciences, University of CambridgeCambridgeUK

Personalised recommendations