On rational points of the generic elliptic curve with level N structure over the field of modular functions of level N

Tetsuji SHIODA

doi:10.2969/jmsj/02510144

Tetsuji SHIODA

著者情報

ジャーナルフリー

1973 年 25 巻 1 号 p. 144-157

DOI https://doi.org/10.2969/jmsj/02510144

詳細

Published: 1973 Received: 1972/04/10 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) P. Deligne, Formes modulaires et représentations l-adiques, Sém. Bourbaki, 1968/69, exp. 355, 1-33.
2) A. Grothendieck, Le groupe de Brauer II, Sém. Bourbaki, 1965/66, exp. 297, 1-21.
3) J. Igusa, On the transformation theory of elliptic modular functions, Amer. J. Math., 81 (1959), 436-452.
4) J. Igusa, Fibre systems of Jacobian varieties (III. Fibre systems of elliptic curves), Amer. J. Math., 81 (1959), 453-476.
5) J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math., 81 (1959), 561-577.
6) J. Igusa, Betti and Picard numbers of abstract algebraic surfaces, Proc. Nat. Acad. Sci., 46 (1960), 724-726.
7) K. Kodaira, On compact analytic surfaces II-III, Ann. of Math., 77 (1963), 563-626; 78 (1963), 1-40.
8) L. J. Mordell, Diophantine equations, Academic Press, London and New York, 1969.
9) D. Mumford, Geometric invariant theory, Springer-Verlag, Berlin-Heidelberg-New York, 1965.
10) A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux etglobaux, Publ. I. H. E. S., No. 21, 1964.
11) A. P. Ogg, Elliptic curves and wild ramification, Amer. J. Math., 89 (1967), 1-21.
12) T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1.972), 20-59 (cited as EMS)).
13) J. Tate, On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, Sém. Bourbaki, 1966, exp. 306, 1-26.
14) A, Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948.
15) A. Weil, Dirichlet series and automorphic forms, Lecture notes No. 189, Springer, 1970.

Right : [1] P. Deligne, Formes modulaires et représentations l-adiques, Sém. Bourbaki, 1968/69, exp. 355, 1-33.
[2] A. Grothendieck, Le groupe de Brauer II, Sém. Bourbaki, 1965/66, exp. 297, 1-21.
[3] J. Igusa, On the transformation theory of elliptic modular functions, Amer. J. Math., 81 (1959), 436-452.
[4] J. Igusa, Fibre systems of Jacobian varieties (III. Fibre systems of elliptic curves), Amer. J. Math., 81 (1959), 453-476.
[5] J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math., 81 (1959), 561-577.
[6] J. Igusa, Betti and Picard numbers of abstract algebraic surfaces, Proc. Nat. Acad. Sci., 46 (1960), 724-726.
[7] K. Kodaira, On compact analytic surfaces II-III, Ann. of Math., 77 (1963), 563-626; 78 (1963), 1-40.
[8] L. J. Mordell, Diophantine equations, Academic Press, London and New York, 1969.
[9] D. Mumford, Geometric invariant theory, Springer-Verlag, Berlin-Heidelberg-New York, 1965.
[10] A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. I. H. E. S., No. 21, 1964.
[11] A. P. Ogg, Elliptic curves and wild ramification, Amer. J. Math., 89 (1967), 1-21.
[12] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 20-59 (cited as EMS)).
[13] J. Tate, On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, Sém. Bourbaki, 1966, exp. 306, 1-26.
[14] A, Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948.
[15] A. Weil, Dirichlet series and automorphic forms, Lecture notes No. 189, Springer, 1970.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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