References
D. Bertrand,Minimal heights and polarizations on abelian varieties, preprint M. S. R. I. 06220-87 (June 1987).
J. W. S. Cassels,Rational quadratic forms, Academic Press, 1978.
C. W. Curtis andI. Reiner,Representation theory of finite groups and associative algebras, Interscience Publishers, 1962.
C. W. Curtis andI. Reiner,Methods of representation theory with applications to finite groups and orders, Vol. I, Wiley-Interscience, 1981.
G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern,Invent. Math.,73 (1983), 349–366.
H. Hasse,Number theory, Springer, 1980.
S. Lang,Abelian varieties, Springer, 1983.
H. W. Lenstra Jr.,F. Oort andY. Zarhin,Abelian subvarieties, preprint University of Utrecht 842 (March 1994).
D. W. Masser andG. Wüstholz, Zero estimates on group varieties II,Invent. Math.,80 (1985), 233–267.
D. W. Masser andG. Wüstholz, Periods and minimal abelian subvarieties,Annals of Math.,137 (1993), 407–458.
D. W. Masser andG. Wüstholz, Isogeny estimates for abelian varieties, and finiteness theorems,Annals of Math.,137 (1993), 459–472.
D. W. Masser andG. Wüstholz, Endomorphism estimates for abelian varieties,Math. Z.,215 (1994), 641–653.
D. Mumford,Abelian varieties, Oxford, 1974.
R. S. Pierce,Associative algebras, Springer, 1982.
I. Reiner,Maximal orders, Academic Press, 1975.
L. Ronyai, Zero divisors in quaternion algebras,J. Algorithms,9 (1988), 494–506.
A. Silverberg, Fields of definition for homomorphisms of abelian varieties,J. Pure and Applied Algebra,77 (1992), 253–262.
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.
Y. Zarhin, A finiteness theorem for unpolarized abelian varieties over number fields with prescribed places of bad reduction,Invent. Math.,79 (1985), 309–321.
Author information
Authors and Affiliations
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02699374