Unirational elliptic surfaces in characteristic 2

Mari OHHIRA

doi:10.2969/jmsj/04440709

Mari OHHIRA

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 4 Pages 709-738

DOI https://doi.org/10.2969/jmsj/04440709

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Published: 1992 Received: December 01, 1989 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) M. Artin, Supersingular K3 surfaces, Ann. Sci. École Norm. Sup. (4), 7 (1974), 543-568.
2) F. R. Cossec and I. V. Dolgachev, Enriques Surfaces I, Birkhäuser, Boston-Basel-Berlin, 1989.
3) R. Hartshorne, Algebraic Geometry, Grad. Texts in Math., 52, Springer, Berlin-Heidelberg-New York, 1977.
4) T. Katsura, Unirational elliptic surfaces in characteristic p, Tohoku. Math. J., 33 (1981), 521-553.
5) T. Katsura, The unirationality of certain elliptic surfaces in characteristic p, Tohoku Math. J., 36 (1984), 217-231.
6) T. Katsura, Generalized Kummer Surfaces and their unirationality in characteristic p, J. Fac. Sci. Univ. Tokyo, 34 (1987), 1-41.
7) S. Lang, Abelian Varieties, Interscience-Wiley, New York, 1959.
8) A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. IHES, 21 (1964).
9) A. P. Ogg, Cohomology of abelian varieties over function fields, Ann. of Math., 76 (1962), 185-212.
10) A. P. Ogg, Elliptic curves and wild ramification, Amer. J. Math., 89 (1967), 1-21.
11) A. N. Rudakov and I. R. Shafarevich, Supersingular K3 surfaces over fields of characteristic 2, Math. USSR-Izv., 13 (1979), 147-165.
12) I. R. Shafarevich, Principal homogeneous spaces defined over a function field, Amer. Math. Soc. Transl. Ser. 2, 37 (1964), 85-114.
13) T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 20-59.
14) T. Shioda, An example of unirational surfaces in characteristic p, Math. Ann., 211 (1974), 233-236.
15) T. Shioda, On unirationality of supersingular surfaces, Math. Ann., 225 (1977), 155-159.
16) T. Shioda, Some results on unirationality of algebraic surfaces, Math. Ann., 230 (1977), 153-168.
17) J. H. Silverman, The arithmetic of elliptic curves, Grad. Texts in Math., 106, Springer, Berlin-Heidelberg-New York, 1986.
18) J. Tate, Algorithm for determining the type of singular fibre in an elliptic pencil, in Modular Function of One Variable IV, Lect. Notes in Math., 476, Springer, Berlin-Heidelberg-New York, 1975, pp. 33-52.

Right : [1] M. Artin, Supersingular K3 surfaces, Ann. Sci. École Norm. Sup. (4), 7 (1974), 543-568.
[2] F. R. Cossec and I. V. Dolgachev, Enriques Surfaces I, Birkhäuser, Boston-Basel-Berlin, 1989.
[3] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math., 52, Springer, Berlin-Heidelberg-New York, 1977.
[4] T. Katsura, Unirational elliptic surfaces in characteristic p, Tôhoku. Math. J., 33 (1981), 521-553.
[5] T. Katsura, The unirationality of certain elliptic surfaces in characteristic p, Tôhoku Math. J., 36 (1984), 217-231.
[6] T. Katsura, Generalized Kummer Surfaces and their unirationality in characteristic p, J. Fac. Sci. Univ. Tokyo, 34 (1987), 1-41.
[7] S. Lang, Abelian Varieties, Interscience-Wiley, New York, 1959.
[8] A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. IHES, 21 (1964).
[9] A. P. Ogg, Cohomology of abelian varieties over function fields, Ann. of Math., 76 (1962), 185-212.
[10] A. P. Ogg, Elliptic curves and wild ramification, Amer. J. Math., 89 (1967), 1-21.
[11] A. N. Rudakov and I. R. Shafarevich, Supersingular K3 surfaces over fields of characteristic 2, Math. USSR-Izv., 13 (1979), 147-165.
[12] I. R. Shafarevich, Principal homogeneous spaces defined over a function field, Amer. Math. Soc. Transl. Ser. 2, 37 (1964), 85-114.
[13] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 20-59.
[14] T. Shioda, An example of unirational surfaces in characteristic p, Math. Ann., 211 (1974), 233-236.
[15] T. Shioda, On unirationality of supersingular surfaces, Math. Ann., 225 (1977), 155-159.
[16] T. Shioda, Some results on unirationality of algebraic surfaces, Math. Ann., 230 (1977), 153-168.
[17] J. H. Silverman, The arithmetic of elliptic curves, Grad. Texts in Math., 106, Springer, Berlin-Heidelberg-New York, 1986.
[18] J. Tate, Algorithm for determining the type of singular fibre in an elliptic pencil, in Modular Function of One Variable IV, Lect. Notes in Math., 476, Springer, Berlin-Heidelberg-New York, 1975, pp. 33-52.

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