This is a preview of subscription content, log in via an institution to check access.
References
Borevich, Z.I., Shafarevich, I.R.: Number theory. New York-London: Academic Press 1966
Deligne, P., Mumford, D.: The irreducibility of the space of curves of given genus. Publ. Math. No.36 (Volume dedicated to O. Zariski), IHÉS, 1969, pp. 75–109
Demazure, M., Gabriel, P.: Groupes algébriques, I. Amsterdam: North-Holland Co. 1970
Demazure, M., Grothendieck, A.: Schémas en groupes fasc. 1.Sém. géom. alg. 1963, IHÉS. Lecture Notes in Mathematics151, Berlin-Heidelberg-New York: Springer 1970
Fulton, W.: Algebraic curves. Math. Lect. Notes Series. New York: Benjamin 1969
Grothendieck, A.: Sém. géom. alg. 1960/61: Revêtements étales et groupe fondamental. Lecture Notes in Mathematics224, Berlin-Heidelberg-New York: Springer 1971
Grothendieck, A., Dieudonné, J.: Éléments de géométrie algébrique. Chap. II. Publ. Math. No. 8,IHÉS, 1961. Cited as EGA
Grothendieck, A.: Uh théorème sur les homomorphismes de schémas abéliens. Inventiones math.,2, 59–78 (1966)
Grothendieck, A., Raynaud, M., Rim, D.S., Deligne, P.: Sém. géom. algébrique, Groupes de monodromie en géométrie algébrique (SGA 7, I). Lecture Notes in Mathematics288, Berlin-Heidelberg-New York: Springer 1972
Hasse, H., Witt, E.: Zyklische unverzweigte Erweiterungskörper vom Primzahlgradep über einem algebraischen Funktionenkörper der Charakteristikp. Monatsh. Math. Physik43, 477–492 (1936)
Honda, T.: Isogeny classes of abelian varieties over finite fields. Journ. Math. Soc. Japan20, 83–95 (1968)
Hoyt, W.L.: On the products and algebraic families of Jacobian varieties. Ann. Math.77, 415–423 (1963)
Igusa, J.-I.: The arithmetic variety of moduli for genus two. Ann. Math.72, 612–649 (1960)
Kas, A.: On deformations of a certain type of irregular algebraic surfaces. Amer. J. Math.90, 789–804 (1968)
Kodaira, K.: A certain type of irregular algebraic surfaces. Journ. Analyse Math.19, 207–215 (1967)
Lang, S.: Abelian varieties. New York: Interscience 1959
Lang, S., Néron, A.: Rational points of abelian varieties over function fields. Amer. Journ. Math.81, 95–118 (1959)
Lenstra, H.W. Jr., Oort, F.: Simple abelian varieties having a prescribed formal isogeny type. To appear in Journ. pure applied Algebra
Manin, Yu.I.: The theory of commutative formal groups over fields of finite characteristic. Russian Math. Surveys18, 1–80 (1963)
Matsusaka, T.: Polarized varieties, the fields of moduli and generalized Kummer varieties of Abelian varieties. Proc. Japan. Acad.32, 367–372 (1956)
Mumford, D.: Geometric invariant theory. Ergebnisse der Mathematik, Neue F. Bd.34, Berlin-Heidelberg-New York: Springer 1965
Mumford, D.: Abelian varieties. Tata Inst. F.R. Stud. in Math. No. 5, Oxford Univ. Press 1970
Oort, F.: Commutative group schemes. Lecture Notes in Mathematics15, Berlin-Heidelberg-New York: Springer 1966
Oort, F.: Finite group schemes, local moduli for abelian varieties, and lifting problems. Comp Math.23, 265–296 (1971) (also: Algebraic geometry, Oslo, 1970, Wolters Noordhoff, 1972)
Oort, F.: Good and stable reduction of abelian varieties. Manuscripta math.11, 171–197 (1974)
Oort, F.: The isogeny class of a CM-type abelian variety is defined over a finite extension of the prime field. To appear in Journ. pure applied Algebra
Oort, F., Ueno, K.: Principally polarized abelian varieties of dimension two or three are Jacobian varieties. Journ. Fac. Sc. Univ. Tokyo,20, 377–381 (1973)
Parshin, A.N.: Algebraic curves over function fields, I. Izv. Akad. Nauk SSSR, Ser. Math.32, 1145–1170 (1968)
Schlessinger, M.: Functors of artin rings, Transact. Amer. Math. Soc.130, 208–222 (1968)
Serre, J.-P.: Groupes algébriques, et corps de classes. Act. Sc. Ind. No. 1264. Paris: Hermann 1959
Serre, J.-P., Tate, J.: Good reduction of abelian varieties, Ann. Math.88, 492–517 (1968)
Shafarevich, I.R.: Principal homogeneous spaces defined over a function field. Amer. Math. Soc. Translat. Ser. 237, 85–114 (1964)
Tate, J.: Endomorphisms of abelian varieties over finite fields. Inventiones math.2, 134–144 (1966)
Waterhouse, W.C.: Abelian varieties over finite fields. Ann. Scient. Éc. Norm. Sup., 4, sér.,2, 521–560 (1969)
Weiss, E.: Algebraic number theory. New York: McGraw Hill 1963
Author information
Authors and Affiliations
Additional information
The University of Aarhus is gratefully thanked for hospitality and excellent working conditions. I thank the referee for some improvements such as a better formulation for Theorem (2.1),and an alternative for the last part of the proof of Theorem (4.2).
Rights and permissions
About this article
Cite this article
Oort, F. Subvarieties of moduli spaces. Invent Math 24, 95–119 (1974). https://doi.org/10.1007/BF01404301
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01404301