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Inventiones mathematicae

, Volume 176, Issue 2, pp 405–447 | Cite as

Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension

  • P. Habegger
Article

Keywords

Line Bundle Elliptic Curve Irreducible Component Abelian Variety Maximal Rank 
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.

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References

  1. 1.
    Ax, J.: Some topics in differential algebraic geometry I: Analytic subgroups of algebraic groups. Am. J. Math. 94, 1195–1204 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bombieri, E., Gubler, W.: Heights in Diophantine Geometry. Cambridge University Press, Cambridge (2006)zbMATHGoogle Scholar
  3. 3.
    Bombieri, E., Masser, D., Zannier, U.: Intersecting a curve with algebraic subgroups of multiplicative groups. Int. Math. Res. Not. 20, 1119–1140 (1999)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bombieri, E., Masser, D., Zannier, U.: Anomalous subvarieties – structure theorems and applications. Int. Math. Res. Not. 19, 1–33 (2007)Google Scholar
  5. 5.
    Bombieri, E., Masser, D., Zannier, U.: Intersecting a plane with algebraic subgroups of multiplicative groups. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 7, 51–80 (2008)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Bombieri, E., Masser, D., Zannier, U.: On unlikely intersections of complex varieties with tori. Acta Arith. (to appear)Google Scholar
  7. 7.
    Carrizosa, M.: Problème de Lehmer et variétés abéliennes CM. C. R. Acad. Sci., Paris, Sér. I (2008). Doi:10.1016/j.crma.2008.10.004Google Scholar
  8. 8.
    Carrizosa, M.: Problème de Lehmer relatif pour les variétés abéliennes CM. Ph.D. thesis, Université Paris 6 (2008)Google Scholar
  9. 9.
    Cassels, J.W.S.: An Introduction to Diophantine Approximation. Cambridge University Press, Cambridge (1965)Google Scholar
  10. 10.
    Danilov, V.I.: Algebraic varieties and schemes. In: Shafarevich, I.R. (ed.) Algebraic Geometry I, Encycl. Math. Sci., vol. 23. Springer, Berlin (1994)Google Scholar
  11. 11.
    Fulton, W.: Intersection Theory. Springer, Berlin (1984)zbMATHGoogle Scholar
  12. 12.
    Grauert, H., Remmert, R.: Coherent Analytic Sheaves. Springer, Berlin (1984)zbMATHGoogle Scholar
  13. 13.
    Habegger, P.: On the bounded height conjecture. Int. Math. Res. Not. (to appear)Google Scholar
  14. 14.
    Lang, S.: Fundamentals of Differential Geometry. Springer, New York (2001)zbMATHGoogle Scholar
  15. 15.
    Lazarsfeld, R.: Positivity in Algebraic Geometry I. Springer, Berlin (2004)Google Scholar
  16. 16.
    Mumford, D.: Abelian Varieties. Oxford University Press, London (1970)zbMATHGoogle Scholar
  17. 17.
    Pink, R.: A common generalization of the conjectures of André–Oort, Manin–Mumford, and Mordell–Lang. PreprintGoogle Scholar
  18. 18.
    Ratazzi, N.: Intersection de courbes et de sous-groupes et problèmes de minoration de hauteur dans les variétés abéliennes C.M. Ann. Inst. Fourier 58(5), 1575–1633 (2008)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Rémond, G.: Intersection de sous-groupes et de sous-variétés I. Math. Ann. 333, 525–548 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Rémond, G.: Intersection de sous-groupes et de sous-variétés II. J. Inst. Math. Jussieu 6(2), 317–348 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Rémond, G.: Intersection de sous-groupes et de sous-variétés III. Comment. Math. Helv. (to appear)Google Scholar
  22. 22.
    Schinzel, A.: Polynomials with Special Regard to Reducibility. With an Appendix by Umberto Zannier. Encycl. Math. Appl., vol. 77. Cambridge University Press, Cambridge (2000)Google Scholar
  23. 23.
    Viada, E.: The intersection of a curve with algebraic subgroups in a product of elliptic curves. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 2, 47–75 (2003)zbMATHMathSciNetGoogle Scholar
  24. 24.
    Weyl, H.: The Classical Groups. Their Invariants and Representations. Princeton University Press, Princeton, NJ (1973)Google Scholar
  25. 25.
    Whitney, H.: Complex Analytic Varieties. Addison-Wesley, Reading, MA (1972)zbMATHGoogle Scholar
  26. 26.
    Zannier, U.: Appendix by Umberto Zannier in [22], pp. 517–539 (2000)Google Scholar
  27. 27.
    Zilber, B.: Exponential sums equations and the Schanuel conjecture. J. Lond. Math. Soc., II. Ser. 65(1), 27–44 (2002)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Departement MathematikETH ZürichZürichSwitzerland

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