The canonical lifting of an ordinary Jacobian variety need not be a Jacobian variety

Frans OORT; Tsutomu SEKIGUCHI

doi:10.2969/jmsj/03830427

Frans OORT, Tsutomu SEKIGUCHI

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 3 Pages 427-437

DOI https://doi.org/10.2969/jmsj/03830427

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Published: 1986 Received: June 18, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Andreotti, On a theorem of Torelli, Amer. J. Math., 80 (1958), 801-828.
2) C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Interscience, New York, 1962.
3) P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Publ. Math. I.H.E.S., 36 (1969), 75-110.
4) N. Katz, Serre-Tate moduli, Surfaces algébriques, Orsay 1976-78, édité par J. Giraud, L. Illusie et M. Raynaud, Lecture Notes in Math., 868, Springer, 1981, pp. 138-202.
5) W. Messing, The crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Lecture Notes in Math., 264, Springer, 1962.
6) D. Mumford, Geometric invariant theory, Ergebn. Math., 34, Springer, 1965.
7) F. Oort, Commutative group schemes, Lecture Notes in Math., 15, Springer, 1966.
8) F. Oort, Finite group schemes, local moduli for abelian varieties, and lifting problems, Compositio Math., 23(1971), 263-296 (also: Algebraic geometry Oslo 1970, F. Oort editor, Wolters-Noordhoff, 1972, pp. 223-254).
9) F. Oort and J. Steenbrink, The local Torelli problem for algebraic curves, Algebraic geometry Angers 1979, A. Beauville editor, Sijthoff-Noordhoff, 1980, pp. 157-203.
10) F. Oort and K. Ueno, Principally polarized abelian varieties of dimension two or three are Jacobian varieties, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 20 (1973), 377-381.
11) T. Sekiguchi, On the fields of rationality for curves and for their Jacobian varieties, Nagoya Math. J., 88 (1982), 197-212.
12) T. Sekiguchi, Wild ramification of moduli spaces for curves or for abelian varieties, Compositio Math., 54 (1985), 331-372.
13) T. Sekiguchi and F. Oort, On the deformation of Artin-Schreier to Kummer, to appear.
14) D. Subrao, The p-rank of Artin-Schreier curves, Manuscripta Math., 16 (1975), 169-193.
15) A. Weil, Zum Beweis des Torellischen Satzes, Nachr. Akad. Wiss. Göttingen, (1957), 33-53.

Right : [1] A. Andreotti, On a theorem of Torelli, Amer. J. Math., 80 (1958), 801-828.
[2] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Interscience, New York, 1962.
[3] P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Publ. Math. I. H. E. S., 36 (1969), 75-110.
[4] N. Katz, Serre-Tate moduli, Surfaces algébriques, Orsay 1976-78, édité par J. Giraud, L. Illusie et M. Raynaud, Lecture Notes in Math., 868, Springer, 1981, pp. 138-202.
[5] W. Messing, The crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Lecture Notes in Math., 264, Springer, 1962.
[6] D. Mumford, Geometric invariant theory, Ergebn. Math., 34, Springer, 1965.
[7] F. Oort, Commutative group schemes, Lecture Notes in Math., 15, Springer, 1966.
[8] F. Oort, Finite group schemes, local moduli for abelian varieties, and lifting problems, Compositio Math., 23 (1971), 263-296 (also: Algebraic geometry Oslo 1970, F. Oort editor, Wolters-Noordhoff, 1972, pp. 223-254).
[9] F. Oort and J. Steenbrink, The local Torelli problem for algebraic curves, Algebraic geometry Angers 1979, A. Beauville editor, Sijthoff-Noordhoff, 1980, pp. 157-203.
[10] F. Oort and K. Ueno, Principally polarized abelian varieties of dimension two or three are Jacobian varieties, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 20 (1973), 377-381.
[11] T. Sekiguchi, On the fields of rationality for curves and for their Jacobian varieties, Nagoya Math. J., 88 (1982), 197-212.
[12] T. Sekiguchi, Wild ramification of moduli spaces for curves or for abelian varieties, Compositio Math., 54 (1985), 331-372.
[13] T. Sekiguchi and F. Oort, On the deformation of Artin-Schreier to Kummer, to appear.
[14] D. Subrao, The p-rank of Artin-Schreier curves, Manuscripta Math., 16 (1975), 169-193.
[15] A. Weil, Zum Beweis des Torellischen Satzes, Nachr. Akad. Wiss. Göttingen, (1957), 33-53.

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