A construction of an abelian variety with a given endomorphism algebra

F. Oort; M. Van der Put

Compositio Mathematica (1988)

  • Volume: 67, Issue: 1, page 103-120
  • ISSN: 0010-437X

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Oort, F., and Van der Put, M.. "A construction of an abelian variety with a given endomorphism algebra." Compositio Mathematica 67.1 (1988): 103-120. <http://eudml.org/doc/89907>.

@article{Oort1988,
author = {Oort, F., Van der Put, M.},
journal = {Compositio Mathematica},
keywords = {existence of abelian varieties of small dimensions; endomorphism algebra; one-parameter family of polarized abelian varieties},
language = {eng},
number = {1},
pages = {103-120},
publisher = {Kluwer Academic Publishers},
title = {A construction of an abelian variety with a given endomorphism algebra},
url = {http://eudml.org/doc/89907},
volume = {67},
year = {1988},
}

TY - JOUR
AU - Oort, F.
AU - Van der Put, M.
TI - A construction of an abelian variety with a given endomorphism algebra
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 67
IS - 1
SP - 103
EP - 120
LA - eng
KW - existence of abelian varieties of small dimensions; endomorphism algebra; one-parameter family of polarized abelian varieties
UR - http://eudml.org/doc/89907
ER -

References

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  1. [F] G. Faltings: Arithmetische Kopaktifizierung des Modulraums der abelsche Varietäten. Lect. N. Mat.1111 (1984) pp. 321-383. Zbl0597.14036MR797429
  2. [G] L. Gerritzen: On multiplicative algebras of Riemann matrices. Math. Ann.194 (1971) 109-122. Zbl0245.14016MR288141
  3. [M1] D. Mumford: Abelian Varieties. Tata Inst. Fund. Research, Bombay, and Oxford Univ. Press (1974). Zbl0326.14012MR282985
  4. [M2] D. Mumford: An analytic construction of degenerating abelian varieties over complete rings. Comp. Math.24 (1972) 239-272. Zbl0241.14020MR352106
  5. [O1] F. Oort: Lifting algebraic curves, abelian varieties and their endomorphisms to characteristic zero. In: S.J. Bloch (ed.) Algebraic Geometry, Bowdoin1985, Proceed. Symp. Pure Math. Vol. 46, Part 2, A.M.S. (1987) pp. 165-195. Zbl0645.14017MR927980
  6. [O2] F. Oort: Endomorphism algebras of abelian varieties. To appear: Algebr. Geom. and Communt. Algebra in Honor of Masayoshi Nagata (1987) pp. 101-134. Zbl0697.14029MR977774
  7. [T] J. Tate: Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda). Sém. Bourbaki21 (1968/69),Exp. 352. Lect. N. Math.179, Springer-Verlag (1971). Zbl0212.25702

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