Mazur, Barry
Modular curves and the Eisenstein ideal
Publications Mathématiques de l'IHÉS, Tome 47 (1977) , p. 33-186
Zbl 0394.14008 | MR 80c:14015 | 53 citations dans Numdam
URL stable : http://www.numdam.org/item?id=PMIHES_1977__47__33_0

Bibliographie

[1] Artin (M.), Grothendieck topologies, Mimeographed notes, Harvard University, 1962. Zbl 0208.48701

[2] Atkin (A. O. L.), Lehner (J.), Hecke operators on Γ0(m), Math. Ann., 185 (1970), 134-160. MR 42 #3022 | Zbl 0177.34901

[3] Bass (H.), On the ubiquity of Gorenstein rings, Math. Zeitschrift, 82 (1963), 8-28. MR 27 #3669 | Zbl 0112.26604

[4] Brumer (A.), Kramer (K.), On the rank of elliptic curves, I (in preparation). Zbl 0376.14011

[5] Cassels (J. W. S.), Fröhlich (A.) (eds.), Algebraic Number Theory, London-New York, Academic Press, 1967. Zbl 0153.07403

[6] Curtis (C. W.), Reiner (I.), Representation theory of finite groups and associative algebras, New York, Interscience, 1962. MR 26 #2519 | Zbl 0131.25601

[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. Numdam | Zbl 0206.49901

[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. Numdam | MR 41 #6850 | Zbl 0181.48803

[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. Zbl 0281.14010

[10] Deligne (P.), Serre (J.-P.), Formes modulaires de poids I, Ann. Scient. Éc. Norm. Sup., 4e série, t. 7 (1974), 507-530. Numdam | MR 52 #284 | Zbl 0321.10026

[11] Demazure (M.), Gabriel (P.), Groupes algébriques, t. I, Amsterdam, North-Holland Publishing Co., 1970. Zbl 0203.23401

[12] Demjanenko (V. A.), Torsion of elliptic curves [in Russian], Izv. Akad. Nauk. CCCP, 35 (1971), 280-307 [MR 44, 2755]. MR 44 #2755 | Zbl 0222.14018

[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. Zbl 0321.14014

[14] Fontaine (J.-M.), Groupes finis commutatifs sur les vecteurs de Witt, C. R. Acad. Sc. Paris, t. 280 (1975), série A, 1423-1425. MR 51 #10353 | Zbl 0331.14023

[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, Zbl 0198.25901

[16] Hadano (T.), On the conductor of an elliptic curve with a rational point of order 2, Nagoya Math. J., 53 (1974), 199-210. MR 50 #7151 | Zbl 0268.14008

[17] Hartshorne (R.), Residues and Duality, Lecture Notes in Mathematics, 20, Berlin-Heidelberg-New York. Springer, 1966. MR 36 #5145 | Zbl 0212.26101

[18] Hartshorne (R.), On the De Rham cohomology of algebraic varieties, Publications Mathématiques I.H.E.S., 45 (1975), 1-99. Numdam | MR 55 #5633 | Zbl 0326.14004

[19] Hecke (E.), Mathematische Werke, 2nd edition, Göttingen, Vandenhoeck & Ruprecht, 1970. MR 51 #7795 | Zbl 0205.28902

[20] Herbrand (J.), Sur les classes des corps circulaires, Journal de Math. pures et appliquées, 9e série, 11 (1932), 417-441. JFM 58.0180.02

[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. MR 51 #8119 | Zbl 0323.14010

[22] Iwasawa (K.), Lectures on p-adic L-functions, Princeton, Princeton University Press and University of Tokyo Press, 1972. MR 50 #12974 | Zbl 0236.12001

[23] Iwasawa (K.), On p-adic L-functions, Ann. Math., 89 (1969), 198-205. MR 42 #4522 | Zbl 0186.09201

[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. MR 56 #5434 | Zbl 0271.10033

[25] Kiepert (L.), Ueber gewisse Vereinfachungen der Transformationsgleichungen in der Theorie der elliptischen Functionen, Math. Ann., 37 (1890), 368-398. JFM 22.0465.02

[26] Koike (M.), On the congruences between Eisenstein series and cusp forms (to appear).

[27] Kubert (D.), Universal bounds on the torsion of elliptic curves, Proc. London Math. Soc. (3), 33 (1976), 193-237. MR 55 #7910 | Zbl 0331.14010

[28] Kubert (D.), Lang (S.), Units in the modular function field, I, II, III, Math. Ann., 218 (1975), 67-96, 175-189, 273-285. MR 55 #10424a | Zbl 0311.14005

[29] Lang (S.), Elliptic Functions, Addison Wesley, Reading, 1974. Zbl 0316.14001

[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. Numdam | Zbl 0322.14011

[31] Manin (Y.), A uniform bound for p-torsion in elliptic curves [in Russian], Izv. Akad. Nauk. CCCP, 33 (1969), 459-465.

[32] Manin (Y.), Parabolic points and zeta functions of modular forms [in Russian], Izv. Akad. Nauk. CCCP, 36 (1972), 19-65. Zbl 0243.14008

[33] Mazur (B.), Notes on étale cohomology of number fields, Ann. Scient. Éc. Norm. Sup., 4e série, t. 6 (1973), 521-556. Numdam | MR 49 #8993 | Zbl 0282.14004

[34] Mazur (B.), Rational points on abelian varieties with values in towers of number fields, Inventiones Math., 18 (1972), 183-266. MR 56 #3020 | Zbl 0245.14015

[35] Mazur (B.), Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, No. 414, Lecture Notes in Mathematics, No. 317, Berlin-Heidelberg-New York, Springer, 1973. Numdam | MR 55 #2930 | Zbl 0276.14012

[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). Zbl 0351.14011

[37] Mazur (B.), Messing (W.), Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Mathematics, No. 370, Berlin-Heidelberg-New York, Springer, 1974. MR 51 #10350 | Zbl 0301.14016

[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. Numdam | Zbl 0346.14013

[39] Mazur (B.), Swinnerton-Dyer (P.), Arithmetic of Weil curves, Inventiones math., 25 (1974), 1-61. MR 50 #7152 | Zbl 0281.14016

[40] Mazur (B.), Tate (J.), Points of order 13 on elliptic curves, Inventiones math., 22 (1973), 41-49. MR 50 #327 | Zbl 0268.14009

[41] Mazur (B.), Vélu (J.), Courbes de Weil de conducteur 26, C. R. Acad. Sc. Paris, t. 275 (1972), série A, 743-745. MR 47 #8551 | Zbl 0241.14015

[42] Miyawaka (I.), Elliptic curves of prime power conductor with Q-rational points of finite order, Osaka J Math., 10 (1973), 309-323. MR 48 #6118 | Zbl 0269.14012

[43] Mumford (D.), Geometric invariant theory, Ergebnisse der Math., 34, Berlin-Heidelberg-New York, Springer, 1965. MR 35 #5451 | Zbl 0147.39304

[44] Mumford (D.), Curves and their jacobians, Ann Arbor, The University of Michigan Press, 1975. MR 54 #7451 | Zbl 0316.14010

[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]. Numdam | MR 31 #3423 | Zbl 0132.41403

[46] Neumann (O.), Elliptische Kurven mit vorgeschriebenem Reduktionsverhalten, I, II, Math. Nachr., 49 (1971), 107-123; Math. Nachr., 56 (1973), 269-280. Zbl 0277.14011

[47] Oda (T.), The first De Rham cohomology group and Dieudonné modules, Ann. scient. Éc. Norm. Sup., 4e série, t. 2 (1969), 63-135. Numdam | MR 39 #2775 | Zbl 0175.47901

[48] Ogg (A.), Rational points on certain elliptic modular curves, Proc. Symp. Pure Math., 24 (1973), 221-231, A.M.S., Providence. MR 49 #2743 | Zbl 0273.14008

[49] Ogg (A.), Diophantine equations and modular forms, Bull. A.M.S., 81 (1975), 14-27. MR 50 #7153 | Zbl 0316.14012

[50] Ogg (A.), Hyperelliptic modular curves, Bull. Soc. Math. France, 102 (1974), 449-462. Numdam | MR 51 #514 | Zbl 0314.10018

[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). Numdam | Zbl 0336.14006

[52] Ohta (M.), On reductions and zeta functions of varieties obtained from Γo(N) (to appear).

[53] Oort (F.), Commutative group schemes, Lecture Notes in Mathematics, No. 15, Berlin-Heidelberg-New York, Springer, 1966. MR 35 #4229 | Zbl 0216.05603

[54] Oort (F.), Tate (J.), Group schemes of prime order, Ann. Scient. Éc. Norm. Sup., série 4, 3 (1970), 1-21. Numdam | MR 42 #278 | Zbl 0195.50801

[55] Raynaud (M.), Schémas en groupes de type (p, ...,p), Bull. Soc. Math. France, 102 (1974), 241-280. Numdam | MR 54 #7488 | Zbl 0325.14020

[56] Raynaud (M.), Spécialisation du foncteur de Picard, Publ. Math. I.H.E.S., 38 (1970), 27-76. Numdam | MR 44 #227 | Zbl 0207.51602

[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. MR 38 #1104 | Zbl 0165.24003

[58] Ribet (K.), Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math., 101 (1975), 555-562. MR 51 #8120 | Zbl 0305.14016

[59] Sen (S.), Lie algebras of Galois groups arising from Hodge-Tate modules, Ann. of Math., 97 (1973), 160-170. MR 47 #3403 | Zbl 0258.12009

[60] Serre (J.-P.), Corps locaux, Paris, Hermann, 1962. MR 27 #133 | Zbl 0137.02601

[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. Zbl 0277.12014

[62] Serre (J.-P.), Algèbre locale. Multiplicités, Lecture Notes in Mathematics, No. 11 (3rd edition), Berlin-Heidelberg-New York, Springer, 1975. MR 34 #1352 | Zbl 0296.13018

[63] Serre (J.-P.), Abelian l-adic representations and elliptic curves, Lectures at McGill University, New York-Amsterdam, W. A. Benjamin Inc., 1968. MR 41 #8422 | Zbl 0186.25701

[64] Serre (J.-P.), Quelques propriétés des variétés abéliennes en caractéristique p, Amer. J. Math., 80 (1958), 715-739. MR 20 #4562 | Zbl 0099.16201

[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. Numdam | Zbl 0222.14019

[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. Numdam | Zbl 0276.14013

[67] Serre (J.-P.), Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Inventiones math., 15 (1972), 259-331. MR 52 #8126 | Zbl 0235.14012

[68] Setzer (B.), Elliptic curves of prime conductor, J. Lond. Math. Soc. (2), 10 (1975), 367-378. MR 51 #8121 | Zbl 0324.14005

[69] Shimura (G.), Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Tokyo-Princeton, 1971. Zbl 0221.10029

[70] Wada (H.), A table of Hecke operators, Proc. Japan Acad., 49 (1973), 380-384. MR 52 #283 | Zbl 0273.10019

[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. MR 50 #7165 | Zbl 0287.14011

[72] Borevich (Z. I.), Shafarevich (I. R.), Number theory, London-New York, Academic Press, 1966. Zbl 0145.04902

[73] Parry (W. R.), A determination of the points which are rational over Q of three modular curves (unpublished). Zbl 0475.14019

[74] Serre (J.-P.), Tate (J.), Good reduction of abelian varieties, Ann. of Math., 88 (1968), 492-517. MR 38 #4488 | Zbl 0172.46101

[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.

[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.

[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. Zbl 0258.00005