Skip to main content
Log in

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. D. Bertrand,Minimal heights and polarizations on abelian varieties, preprint M. S. R. I. 06220-87 (June 1987).

  2. J. W. S. Cassels,Rational quadratic forms, Academic Press, 1978.

  3. C. W. Curtis andI. Reiner,Representation theory of finite groups and associative algebras, Interscience Publishers, 1962.

  4. C. W. Curtis andI. Reiner,Methods of representation theory with applications to finite groups and orders, Vol. I, Wiley-Interscience, 1981.

  5. G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern,Invent. Math.,73 (1983), 349–366.

    Article  Google Scholar 

  6. H. Hasse,Number theory, Springer, 1980.

  7. S. Lang,Abelian varieties, Springer, 1983.

  8. H. W. Lenstra Jr.,F. Oort andY. Zarhin,Abelian subvarieties, preprint University of Utrecht 842 (March 1994).

  9. D. W. Masser andG. Wüstholz, Zero estimates on group varieties II,Invent. Math.,80 (1985), 233–267.

    Article  MATH  Google Scholar 

  10. D. W. Masser andG. Wüstholz, Periods and minimal abelian subvarieties,Annals of Math.,137 (1993), 407–458.

    Article  Google Scholar 

  11. D. W. Masser andG. Wüstholz, Isogeny estimates for abelian varieties, and finiteness theorems,Annals of Math.,137 (1993), 459–472.

    Article  MATH  Google Scholar 

  12. D. W. Masser andG. Wüstholz, Endomorphism estimates for abelian varieties,Math. Z.,215 (1994), 641–653.

    Article  MATH  Google Scholar 

  13. D. Mumford,Abelian varieties, Oxford, 1974.

  14. R. S. Pierce,Associative algebras, Springer, 1982.

  15. I. Reiner,Maximal orders, Academic Press, 1975.

  16. L. Ronyai, Zero divisors in quaternion algebras,J. Algorithms,9 (1988), 494–506.

    Article  MATH  Google Scholar 

  17. A. Silverberg, Fields of definition for homomorphisms of abelian varieties,J. Pure and Applied Algebra,77 (1992), 253–262.

    Article  MATH  Google Scholar 

  18. Y. Zarhin, Endomorphisms of abelian varieties and points of finite order in characteristicp, Mat. Zametki,21 (1977), 737–744;Math. Notes,21 (1977), 415–419.

    Google Scholar 

  19. Y. Zarhin, A finiteness theorem for unpolarized abelian varieties over number fields with prescribed places of bad reduction,Invent. Math.,79 (1985), 309–321.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

To Wolfgang Schmidt, with respect and admiration, on the occasion of his 60th birthday.

About this article

Cite this article

Masser, D.W., Wüstholz, G. Factorization estimates for abelian varieties. Publications Mathématiques de l’Institut des Hautes Scientifiques 81, 5–24 (1995). https://doi.org/10.1007/BF02699374

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02699374

Keywords

Navigation