Rational points on the modular curves X+0(N)

Fumiyuki MOMOSE

doi:10.2969/jmsj/03920269

Rational points on the modular curves X⁺₀(N)

Fumiyuki MOMOSE

著者情報

ジャーナルフリー

1987 年 39 巻 2 号 p. 269-286

DOI https://doi.org/10.2969/jmsj/03920269

詳細

Published: 1987 Received: 1984/01/05 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
2) V. G. Berkovic, The rational points on the jacobians of modular curves, Math. USSR Sbornik, 30-4 (1976), 485-500.
3) P. Deligne and M. Rapoport, Schémas de modules des courbes elliptiques, Proc. International Summer School on Modular Functions, Antwerp 1972, Vol. II, Lecture Notes in Math., 349, Springer, 1973.
4) N. Ishii and F. Momose, Hyperelliptic modular curves, to appear.
5) M. A. Kenku, The modular curve X₀(39) and rational isogeny, Math. Proc. Cambridge Philos. Soc., 85 (1979), 21-23.
6) M. A. Kenku, The modular curves X₀(65) and X₀(91) and rational isogeny, Math. Cambridge Philos. Soc., 87 (1980), 15-20.
7) M. A. Kenku, The modular curve X₀(169) and rational isogeny, J. London Math. Soc. (2), 22 (1980), 239-244.
8) M. A. Kenku, On the modular curves X₀(125), X₁(25) and X₁(49), J. London Math. Soc. (2), 23 (1981), 415-427.
9) B. Mazur, Modular curves and the Eisenstein ideals, Publ. Math. I.H.E.S., 47, 1977.
10) B. Mazur, Rational isogenies of prime degree, Invent. Math., 44 (1978), 129-162.
11) B. Mazur and H. P. F. Swinnerton-Deyer, Arithmetic of Weil curves, Invent. Math., 25 (1974), 1-61.
12) J. F. Mestre, Points rationnels de la courbe modulaire X₀(169), Ann. Inst. Fourier (Grenoble), 30-2 (1980), 17-27.
13) F. Momose, Rational points on the modular curves X_split(p), Compositio Math., 52 (1984), 115-137.
14) F. Momose, Rational points on the modular curves X⁺₀(p^r), to appear.
15) A. Ogg, Über die Automorphismengruppe von X₀(N), Math. Ann., 228 (1977), 279-292.
16) A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France, 102 (1974), 449-462.
17) F. Oort and J. Tate, Group schemes of prime order, Ann. Sci. École Norm. Sup. (4), 3(1970), 1-21.
18) M. Raynaud, Spécialisation du foncteur de Picard, Publ. Math. I.H.E.S., 38, 1970, pp. 27-76.
19) M. Raynaud, Schémas en groupes de type (p, ..., p), Bull. Soc. Math. France, 102 (1974), 241-280.
20) K. A. Ribet, Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math., 101 (1975), 555-562.
21) J. P. Serre, Propriétés galoissiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15 (1972), 259-331.
22) B. J. Birch and W. Kuyk ed., Modular functions of one variable IV, Lecture Notes in Math., 476, Springer, 1975.

Right : [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
[2] V. G. Berkovic, The rational points on the jacobians of modular curves, Math. USSR Sbornik, 30-4 (1976), 485-500.
[3] P. Deligne and M. Rapoport, Schémas de modules des courbes elliptiques, Proc. International Summer School on Modular Functions, Antwerp 1972, Vol. II, Lecture Notes in Math., 349, Springer, 1973.
[4] N. Ishii and F. Momose, Hyperelliptic modular curves, to appear.
[5] M. A. Kenku, The modular curve X₀(39) and rational isogeny, Math. Proc. Cambridge Philos. Soc., 85 (1979), 21-23.
[6] M. A. Kenku, The modular curves X₀(65) and X₀(91) and rational isogeny, Math. Cambridge Philos. Soc., 87 (1980), 15-20.
[7] M. A. Kenku, The modular curve X₀(169) and rational isogeny, J. London Math. Soc. (2), 22 (1980), 239-244.
[8] M. A. Kenku, On the modular curves X₀(125), X₁(25) and X₁(49), J. London Math. Soc. (2), 23 (1981), 415-427.
[9] B. Mazur, Modular curves and the Eisenstein ideals, Publ. Math. I. H. E. S., 47, 1977.
[10] B. Mazur, Rational isogenies of prime degree, Invent. Math., 44 (1978), 129-162.
[11] B. Mazur and H. P. F. Swinnerton-Deyer, Arithmetic of Weil curves, Invent. Math., 25 (1974), 1-61.
[12] J. F. Mestre, Points rationnels de la courbe modulaire X₀(169), Ann. Inst. Fourier (Grenoble), 30-2 (1980), 17-27.
[13] F. Momose, Rational points on the modular curves X_split(p), Compositio Math., 52 (1984), 115-137.
[14] F. Momose, Rational points on the modular curves X⁺₀(p^r), to appear.
[15] A. Ogg, Über die Automorphismengruppe von X₀(N), Math. Ann., 228 (1977), 279-292.
[16] A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France, 102 (1974), 449-462.
[17] F. Oort and J. Tate, Group schemes of prime order, Ann. Sci. École Norm. Sup. (4), 3 (1970), 1-21.
[18] M. Raynaud, Spécialisation du foncteur de Picard, Publ. Math. I. H. E. S., 38, 1970, pp. 27-76.
[19] M. Raynaud, Schémas en groupes de type (p,…,p), Bull. Soc. Math. France, 102 (1974), 241-280.
[20] K. A. Ribet, Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math., 101 (1975), 555-562.
[21] J. P. Serre, Propriétés galoissiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15 (1972), 259-331.
[22] B. J. Birch and W. Kuyk ed., Modular functions of one variable IV, Lecture Notes in Math., 476, Springer, 1975.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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