Modular curves and the Eisenstein ideal

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1. [1] ARTIN (M.), Grothendieck topologies, Mimeographed notes, Harvard University, 1962. Zbl0208.48701
2. [2] ATKIN (A. O. L.), LEHNER (J.), Hecke operators on Γ0(m), Math. Ann., 185 (1970), 134-160. Zbl0177.34901MR42 #3022
3. [3] BASS (H.), On the ubiquity of Gorenstein rings, Math. Zeitschrift, 82 (1963), 8-28. Zbl0112.26604MR27 #3669
4. [4] BRUMER (A.), KRAMER (K.), On the rank of elliptic curves, I (in preparation). Zbl0376.14011
5. [5] CASSELS (J. W. S.), FRÖHLICH (A.) (eds.), Algebraic Number Theory, London-New York, Academic Press, 1967. Zbl0153.07403
6. [6] CURTIS (C. W.), REINER (I.), Representation theory of finite groups and associative algebras, New York, Interscience, 1962. Zbl0131.25601MR26 #2519
7. [7] DELIGNE (P.), Formes modulaires et représentations l-adiques. Séminaire Bourbaki 68-69, no. 355, Lecture Notes in Mathematics, 179, Berlin-Heidelberg-New York, Springer, 1971, 136-172. Zbl0206.49901
8. [8] DELIGNE (P.), MUMFORD (D.), The irreducibility of the space of curves of given genus, Publications Mathématiques I.H.E.S., 36 (1969), 75-109. Zbl0181.48803MR41 #6850
9. [9] DELIGNE (P.), RAPOPORT (M.), Schémas de modules des courbes elliptiques. Vol. II of the Proceedings of the International Summer School on Modular Functions, Antwerp (1972), Lecture Notes in Mathematics, 349, Berlin-Heidelberg-New York, Springer, 1973. Zbl0281.14010
10. [10] DELIGNE (P.), SERRE (J.-P.), Formes modulaires de poids I, Ann. Scient. Éc. Norm. Sup., 4e série, t. 7 (1974), 507-530. Zbl0321.10026MR52 #284
11. [11] DEMAZURE (M.), GABRIEL (P.), Groupes algébriques, t. I, Amsterdam, North-Holland Publishing Co., 1970. Zbl0203.23401
12. [12] DEMJANENKO (V. A.), Torsion of elliptic curves [in Russian], Izv. Akad. Nauk. CCCP, 35 (1971), 280-307 [MR 44, 2755]. Zbl0222.14018MR44 #2755
13. [13] DRINFELD (G. I.), Elliptic modules [in Russian], Mat. Sbornik, 94 (136) (1974), No. 4. Engl. Trans.: A.M.S., vol. 23 (1976), 561-592. Zbl0321.14014
14. [14] FONTAINE (J.-M.), Groupes finis commutatifs sur les vecteurs de Witt, C. R. Acad. Sc. Paris, t. 280 (1975), série A, 1423-1425. Zbl0331.14023MR51 #10353
15. [15] GROTHENDIECK (A.), Le groupe de Brauer III: exemples et compléments (a continuation of Bourbaki exposés: 200, 297). Published in Dix exposés sur la cohomologie des schémas, Amsterdam, North-Holland Publ. Co., 1968, Zbl0198.25901
16. [16] HADANO (T.), On the conductor of an elliptic curve with a rational point of order 2, Nagoya Math. J., 53 (1974), 199-210. Zbl0268.14008MR50 #7151
17. [17] HARTSHORNE (R.), Residues and Duality, Lecture Notes in Mathematics, 20, Berlin-Heidelberg-New York. Springer, 1966. Zbl0212.26101MR36 #5145
18. [18] HARTSHORNE (R.), On the De Rham cohomology of algebraic varieties, Publications Mathématiques I.H.E.S., 45 (1975), 1-99. Zbl0326.14004MR55 #5633
19. [19] HECKE (E.), Mathematische Werke, 2nd edition, Göttingen, Vandenhoeck & Ruprecht, 1970. Zbl0205.28902MR51 #7795
20. [20] HERBRAND (J.), Sur les classes des corps circulaires, Journal de Math. pures et appliquées, 9e série, 11 (1932), 417-441. Zbl58.0180.02JFM58.0180.02
21. [21] IMAI (H.), A remark on the rational points of abelian varieties with values in cyclotomic Zp-extensions, Proc. Japan Acad., 51 (1975), 12-16. Zbl0323.14010MR51 #8119
22. [22] IWASAWA (K.), Lectures on p-adic L-functions, Princeton, Princeton University Press and University of Tokyo Press, 1972. Zbl0236.12001MR50 #12974
23. [23] IWASAWA (K.), On p-adic L-functions, Ann. Math., 89 (1969), 198-205. Zbl0186.09201MR42 #4522
24. [24] KATZ (N.), p-adic properties of modular schemes and modular forms, vol. III of The Proceedings of the International Summer School on Modular Functions, Antwerp (1972), Lecture Notes in Mathematics, 350, Berlin-Heidelberg-New York, Springer, 1973, 69-190. Zbl0271.10033MR56 #5434
25. [25] KIEPERT (L.), Ueber gewisse Vereinfachungen der Transformationsgleichungen in der Theorie der elliptischen Functionen, Math. Ann., 37 (1890), 368-398. Zbl22.0465.02JFM22.0465.02
26. [26] KOIKE (M.), On the congruences between Eisenstein series and cusp forms (to appear). Zbl06400934
27. [27] KUBERT (D.), Universal bounds on the torsion of elliptic curves, Proc. London Math. Soc. (3), 33 (1976), 193-237. Zbl0331.14010MR55 #7910
28. [28] KUBERT (D.), LANG (S.), Units in the modular function field, I, II, III, Math. Ann., 218 (1975), 67-96, 175-189, 273-285. Zbl0311.14005MR55 #10424a
29. [29] LANG (S.), Elliptic Functions, Addison Wesley, Reading, 1974. Zbl0316.14001
30. [30] LIGOZAT (G.), Fonctions L des courbes modulaires, Séminaire Delange-Pisot-Poitou, Jan. 1970. Thesis : Courbes modulaires de genre I, Bull. Soc. math. France, mémoire 43, 1975. Zbl0322.14011
31. [31] MANIN (Y.), A uniform bound for p-torsion in elliptic curves [in Russian], Izv. Akad. Nauk. CCCP, 33 (1969), 459-465. 
32. [32] MANIN (Y.), Parabolic points and zeta functions of modular forms [in Russian], Izv. Akad. Nauk. CCCP, 36 (1972), 19-65. Zbl0243.14008
33. [33] MAZUR (B.), Notes on étale cohomology of number fields, Ann. Scient. Éc. Norm. Sup., 4e série, t. 6 (1973), 521-556. Zbl0282.14004MR49 #8993
34. [34] MAZUR (B.), Rational points on abelian varieties with values in towers of number fields, Inventiones Math., 18 (1972), 183-266. Zbl0245.14015MR56 #3020
35. [35] MAZUR (B.), Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, No. 414, Lecture Notes in Mathematics, No. 317, Berlin-Heidelberg-New York, Springer, 1973. Zbl0276.14012MR55 #2930
36. [36] MAZUR (B.), p-adic analytic number theory of elliptic curves and abelian varieties over Q, Proc. of International Congress of Mathematicians at Vancouver, 1974, vol. I, 369-377, Canadian Math. Soc. (1975). Zbl0351.14011
37. [37] MAZUR (B.), MESSING (W.), Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Mathematics, No. 370, Berlin-Heidelberg-New York, Springer, 1974. Zbl0301.14016MR51 #10350
38. [38] MAZUR (B.), SERRE (J.-P.), Points rationnels des courbes modulaires Xo(N). Séminaire Bourbaki, No. 469, Lecture Notes in Mathematics, No. 514, Berlin-Heidelberg-New York, Springer, 1976. Zbl0346.14013
39. [39] MAZUR (B.), SWINNERTON-DYER (P.), Arithmetic of Weil curves, Inventiones math., 25 (1974), 1-61. Zbl0281.14016MR50 #7152
40. [40] MAZUR (B.), TATE (J.), Points of order 13 on elliptic curves, Inventiones math., 22 (1973), 41-49. Zbl0268.14009MR50 #327
41. [41] MAZUR (B.), VÉLU (J.), Courbes de Weil de conducteur 26, C. R. Acad. Sc. Paris, t. 275 (1972), série A, 743-745. Zbl0241.14015MR47 #8551
42. [42] MIYAWAKA (I.), Elliptic curves of prime power conductor with Q-rational points of finite order, Osaka J Math., 10 (1973), 309-323. Zbl0269.14012MR48 #6118
43. [43] MUMFORD (D.), Geometric invariant theory, Ergebnisse der Math., 34, Berlin-Heidelberg-New York, Springer, 1965. Zbl0147.39304MR35 #5451
44. [44] MUMFORD (D.), Curves and their jacobians, Ann Arbor, The University of Michigan Press, 1975. Zbl0316.14010MR54 #7451
45. [45] NÉRON (A.), Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. I.H.E.S., 21 (1964), 361-483 [MR 31, 3424]. Zbl0132.41403MR31 #3423
46. [46] NEUMANN (O.), Elliptische Kurven mit vorgeschriebenem Reduktionsverhalten, I, II, Math. Nachr., 49 (1971), 107-123; Math. Nachr., 56 (1973), 269-280. Zbl0277.14011
47. [47] ODA (T.), The first De Rham cohomology group and Dieudonné modules, Ann. scient. Éc. Norm. Sup., 4e série, t. 2 (1969), 63-135. Zbl0175.47901MR39 #2775
48. [48] OGG (A.), Rational points on certain elliptic modular curves, Proc. Symp. Pure Math., 24 (1973), 221-231, A.M.S., Providence. Zbl0273.14008MR49 #2743
49. [49] OGG (A.), Diophantine equations and modular forms, Bull. A.M.S., 81 (1975), 14-27. Zbl0316.14012MR50 #7153
50. [50] OGG (A.), Hyperelliptic modular curves, Bull. Soc. Math. France, 102 (1974), 449-462. Zbl0314.10018MR51 #514
51. [51] OGG (A.), Automorphismes des courbes modulaires, Séminaire Delange-Pisot-Poitou, déc. 1974 (mimeo. notes distributed by Secrétariat mathématique, 11, rue Pierre-et-Marie-Curie, 75231 Paris, Cedex 05). Zbl0336.14006
52. [52] OHTA (M.), On reductions and zeta functions of varieties obtained from Γo(N) (to appear). 
53. [53] OORT (F.), Commutative group schemes, Lecture Notes in Mathematics, No. 15, Berlin-Heidelberg-New York, Springer, 1966. Zbl0216.05603MR35 #4229
54. [54] OORT (F.), TATE (J.), Group schemes of prime order, Ann. Scient. Éc. Norm. Sup., série 4, 3 (1970), 1-21. Zbl0195.50801MR42 #278
55. [55] RAYNAUD (M.), Schémas en groupes de type (p, ...,p), Bull. Soc. Math. France, 102 (1974), 241-280. Zbl0325.14020MR54 #7488
56. [56] RAYNAUD (M.), Spécialisation du foncteur de Picard, Publ. Math. I.H.E.S., 38 (1970), 27-76. Zbl0207.51602MR44 #227
57. [57] RAYNAUD (M.), Passage au quotient par une relation d'équivalence plate, Proc. of a Conference on Local Fields, NUFFIC Summer School held at Driebergen in 1966, 133-157, Berlin-Heidelberg-New York, Springer, 1967. Zbl0165.24003MR38 #1104
58. [58] RIBET (K.), Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math., 101 (1975), 555-562. Zbl0305.14016MR51 #8120
59. [59] SEN (S.), Lie algebras of Galois groups arising from Hodge-Tate modules, Ann. of Math., 97 (1973), 160-170. Zbl0258.12009MR47 #3403
60. [60] SERRE (J.-P.), Corps locaux, Paris, Hermann, 1962. Zbl0137.02601MR27 #133
61. [61] SERRE (J.-P.), Formes modulaires et fonctions zêta p-adiques, vol. III of the Proceedings of the International Summer School on Modular Functions, Antwerp (1972), Lecture Notes in Mathematics, 350, 191-268, Berlin-Heidelberg-New York, Springer, 1973. Zbl0277.12014
62. [62] SERRE (J.-P.), Algèbre locale. Multiplicités, Lecture Notes in Mathematics, No. 11 (3rd edition), Berlin-Heidelberg-New York, Springer, 1975. Zbl0296.13018MR34 #1352
63. [63] SERRE (J.-P.), Abelian l-adic representations and elliptic curves, Lectures at McGill University, New York-Amsterdam, W. A. Benjamin Inc., 1968. Zbl0186.25701MR41 #8422
64. [64] SERRE (J.-P.), Quelques propriétés des variétés abéliennes en caractéristique p, Amer. J. Math., 80 (1958), 715-739. Zbl0099.16201MR20 #4562
65. [65] SERRE (J.-P.), p-torsion des courbes elliptiques (d'après Y. Manin). Séminaire Bourbaki, 69-70, No. 380, Lecture Notes in Mathematics, No. 180, Berlin-Heidelberg-New York, Springer, 1971. Zbl0222.14019
66. [66] SERRE (J.-P.), Congruences et formes modulaires (d'après H. P. F. Swinnerton-Dyer). Séminaire Bourbaki, 71-72, N° 416, Lecture Notes in Mathematics, No. 317, Berlin-Heidelberg-New York, Springer, 1973. Zbl0276.14013
67. [67] SERRE (J.-P.), Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Inventiones math., 15 (1972), 259-331. Zbl0235.14012MR52 #8126
68. [68] SETZER (B.), Elliptic curves of prime conductor, J. Lond. Math. Soc. (2), 10 (1975), 367-378. Zbl0324.14005MR51 #8121
69. [69] SHIMURA (G.), Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Tokyo-Princeton, 1971. Zbl0221.10029
70. [70] WADA (H.), A table of Hecke operators, Proc. Japan Acad., 49 (1973), 380-384. Zbl0273.10019MR52 #283
71. [71] YAMAUCHI (M.), On the fields generated by certain points of finite order on Shimura's elliptic curves, J. Math. Kyoto Univ., 14 (2) (1974), 243-255. Zbl0287.14011MR50 #7165
72. [72] BOREVICH (Z. I.), SHAFAREVICH (I. R.), Number theory, London-New York, Academic Press, 1966. Zbl0145.04902
73. [73] PARRY (W. R.), A determination of the points which are rational over Q of three modular curves (unpublished). Zbl0475.14019
74. [74] SERRE (J.-P.), TATE (J.), Good reduction of abelian varieties, Ann. of Math., 88 (1968), 492-517. Zbl0172.46101MR38 #4488
75. [75] TATE (J.), Algorithm for determining the type of a singular fiber in an elliptic pencil, vol. IV of The Proceedings of the International Summer School on Modular Functions, Antwerp (1972), Lecture Notes in Mathematics, 476, Berlin-Heidelberg-New York, Springer, 1975. 
76. [SGA 3] Séminaire de Géométrie algébrique du Bois-Marie, 62-64. Directed by M. DEMAZURE and A. GROTHENDIECK, Lecture Notes in Mathematics, Nos. 151, 152, 153, Berlin-Heidelberg-New York, Springer, 1970. 
77. [SGA 7] Séminaire de Géométrie algébrique du Bois-Marie, 67-69. P. DELIGNE and N. KATZ, Lecture Notes in Mathematics, Nos. 288, 340, Berlin-Heidelberg-New York, Springer, 1972, 1973. Zbl0258.00005

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