Factorization estimates for abelian varieties

D. W. Masser; G. Wüstholz

Publications Mathématiques de l'IHÉS (1995)

  • Volume: 81, page 5-24
  • ISSN: 0073-8301

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Masser, D. W., and Wüstholz, G.. "Factorization estimates for abelian varieties." Publications Mathématiques de l'IHÉS 81 (1995): 5-24. <http://eudml.org/doc/104105>.

@article{Masser1995,
author = {Masser, D. W., Wüstholz, G.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {factorization estimates; abelian varieties; Faltings height; isogeny; class indices; Rosati discriminants; endomorphism estimates},
language = {eng},
pages = {5-24},
publisher = {Institut des Hautes Études Scientifiques},
title = {Factorization estimates for abelian varieties},
url = {http://eudml.org/doc/104105},
volume = {81},
year = {1995},
}

TY - JOUR
AU - Masser, D. W.
AU - Wüstholz, G.
TI - Factorization estimates for abelian varieties
JO - Publications Mathématiques de l'IHÉS
PY - 1995
PB - Institut des Hautes Études Scientifiques
VL - 81
SP - 5
EP - 24
LA - eng
KW - factorization estimates; abelian varieties; Faltings height; isogeny; class indices; Rosati discriminants; endomorphism estimates
UR - http://eudml.org/doc/104105
ER -

References

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  1. [B] D. BERTRAND, Minimal heights and polarizations on abelian varieties, preprint M.S.R.I. 06220-87 (June 1987). 
  2. [Ca] J. W. S. CASSELS, Rational quadratic forms, Academic Press, 1978. Zbl0395.10029MR80m:10019
  3. [CR1] C. W. CURTIS and I. REINER, Representation theory of finite groups and associative algebras, Interscience Publishers, 1962. Zbl0131.25601MR26 #2519
  4. [CR2] C. W. CURTIS and I. REINER, Methods of representation theory with applications to finite groups and orders, Vol. I, Wiley-Interscience, 1981. Zbl0469.20001
  5. [F] G. FALTINGS, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., 73 (1983), 349-366. Zbl0588.14026MR85g:11026a
  6. [H] H. HASSE, Number theory, Springer, 1980. Zbl0423.12002MR81c:12001b
  7. [La] S. LANG, Abelian varieties, Springer, 1983. Zbl0516.14031MR84g:14041
  8. [LOZ] H. W. LENSTRA Jr., F. OORT and Y. ZARHIN, Abelian subvarieties, preprint University of Utrecht 842 (March 1994). 
  9. [MW1] D. W. MASSER and G. WÜSTHOLZ, Zero estimates on group varieties II, Invent. Math., 80 (1985), 233-267. Zbl0564.10041MR86h:11054
  10. [MW2] D. W. MASSER and G. WÜSTHOLZ, Periods and minimal abelian subvarieties, Annals of Math., 137 (1993), 407-458. Zbl0796.11023MR94g:11040
  11. [MW3] D. W. MASSER and G. WÜSTHOLZ, Isogeny estimates for abelian varieties, and finiteness theorems, Annals of Math., 137 (1993), 459-472. Zbl0804.14019MR95d:11074
  12. [MW4] D. W. MASSER and G. WÜSTHOLZ, Endomorphism estimates for abelian varieties, Math. Z., 215 (1994), 641-653. Zbl0826.14025MR95b:14032
  13. [Mu] D. MUMFORD, Abelian varieties, Oxford, 1974. 
  14. [P] R. S. PIERCE, Associative algebras, Springer, 1982. Zbl0497.16001MR84c:16001
  15. [Re] I. REINER, Maximal orders, Academic Press, 1975. Zbl0305.16001MR52 #13910
  16. [Ro] L. RONYAI, Zero divisors in quaternion algebras, J. Algorithms, 9 (1988), 494-506. Zbl0662.12015MR90f:11102
  17. [S] A. SILVERBERG, Fields of definition for homomorphisms of abelian varieties, J. Pure and Applied Algebra, 77 (1992), 253-262. Zbl0808.14037MR93f:14022
  18. [Z1] Y. ZARHIN, Endomorphisms of abelian varieties and points of finite order in characteristic p, Mat. Zametki, 21 (1977), 737-744 ; Math. Notes, 21 (1977), 415-419. Zbl0399.14027
  19. [Z2] Y. ZARHIN, A finiteness theorem for unpolarized abelian varieties over number fields with prescribed places of bad reduction, Invent. Math., 79 (1985), 309-321. Zbl0557.14024MR86d:14041

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