Israel Journal of Mathematics

, Volume 101, Issue 1, pp 85–91 | Cite as

Lang maps and Harris’s conjecture

  • Dan Abramovich


We show that any variety in characteristic 0 possesses a universal dominant rational map, which we callthe Lang map, to a variety of general type. We discuss a conjecture of J. Harris regarding the relation between rational points and Lang maps.


General Type Rational Point Number Field Root Number Generic Fiber 
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. [ℵ] D. Abramovich,Uniformité des points rationnels des courbes algébriques sur les extensions quadratiques et cubiques, Comptes Rendus de l’Académie des Sciences, Paris321 (1995), 755–758.MATHMathSciNetGoogle Scholar
  2. [G-M] G. Grant and E. Manduchi,Root numbers and algebraic points on elliptic surfaces, preprint.Google Scholar
  3. [H1] J. Harris,Lang dimension?, Letter to D. A., L. Caporaso and B. Mazur, Jan. 2, 1995.Google Scholar
  4. [H2] J. Harris,Lang on steroids, Letter to D. A., L. Caporaso and B. Mazur, Jan. 3, 1995.Google Scholar
  5. [Ko:FlAb] J. Kollár,Flips and Abundance for algebraic threefolds, Astérisque211 (1992).Google Scholar
  6. [Ko-Mi-Mo] J. Kollár, Y. Miyaoka and S. Mori,Rationally connected varieties, Journal of Algebraic Geometry1 (1992), 429–448.MATHMathSciNetGoogle Scholar
  7. [L] S. Lang,Hyperbolic diophantine analysis, Bulletin of the American Mathematical Society14 (1986), 159–205.MATHGoogle Scholar
  8. [L:AV] S. Lang,Abelian Varieties, Interscience, New York, 1959.Google Scholar
  9. [Man] E. Manduchi,Root numbers of fibers of elliptic surfaces, Compositio Mathematica99 (1995), 33–58.MATHMathSciNetGoogle Scholar
  10. [MD-LM] M. Martin-Deschamps and R. Lewin-Ménégaux,Applications rationnelles séparables dominantes sur une variété de type général, Bulletin de la Société Mathématique de France106 (1978), 279–287.MATHGoogle Scholar
  11. [Mor] A. Moriwaki,Remarks on S. Lang's conjecture over function fields, preprint. Scholar
  12. [V1] E. Viehweg,Die Additivität der Kodaira Dimension für projektive Fasserräume über Varietäten des allgemeinen Typs, Journal für die reine und angewandte Mathematik330 (1982), 132–142.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Hebrew University 1997

Authors and Affiliations

  1. 1.Department of MathematicsBoston UniversityBostonUSA

Personalised recommendations