@article{PMIHES_1977__47__33_0, author = {Mazur, Barry}, title = {Modular curves and the {Eisenstein} ideal}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {33--186}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {47}, year = {1977}, mrnumber = {488287}, zbl = {0394.14008}, language = {en}, url = {http://www.numdam.org/item/PMIHES_1977__47__33_0/} }
Mazur, Barry. Modular curves and the Eisenstein ideal. Publications Mathématiques de l'IHÉS, Volume 47 (1977), pp. 33-186. http://www.numdam.org/item/PMIHES_1977__47__33_0/
[1] Grothendieck topologies, Mimeographed notes, Harvard University, 1962. | Zbl
,[2] Hecke operators on Γ0(m), Math. Ann., 185 (1970), 134-160. | MR | Zbl
, ,[3] On the ubiquity of Gorenstein rings, Math. Zeitschrift, 82 (1963), 8-28. | MR | Zbl
,[4] On the rank of elliptic curves, I (in preparation). | Zbl
, ,[5] Algebraic Number Theory, London-New York, Academic Press, 1967. | Zbl
, (eds.),[6] Representation theory of finite groups and associative algebras, New York, Interscience, 1962. | MR | Zbl
, ,[7] 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
,[8] The irreducibility of the space of curves of given genus, Publications Mathématiques I.H.E.S., 36 (1969), 75-109. | Numdam | MR | Zbl
, ,[9] 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
, ,[10] Formes modulaires de poids I, Ann. Scient. Éc. Norm. Sup., 4e série, t. 7 (1974), 507-530. | Numdam | MR | Zbl
, ,[11] Groupes algébriques, t. I, Amsterdam, North-Holland Publishing Co., 1970. | Zbl
, ,[12] Torsion of elliptic curves [in Russian], Izv. Akad. Nauk. CCCP, 35 (1971), 280-307 [MR 44, 2755]. | MR | Zbl
,[13] Elliptic modules [in Russian], Mat. Sbornik, 94 (136) (1974), No. 4. Engl. Trans.: A.M.S., vol. 23 (1976), 561-592. | Zbl
,[14] Groupes finis commutatifs sur les vecteurs de Witt, C. R. Acad. Sc. Paris, t. 280 (1975), série A, 1423-1425. | MR | Zbl
,[15] 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
,[16] On the conductor of an elliptic curve with a rational point of order 2, Nagoya Math. J., 53 (1974), 199-210. | MR | Zbl
,[17] Residues and Duality, Lecture Notes in Mathematics, 20, Berlin-Heidelberg-New York. Springer, 1966. | MR | Zbl
,[18] On the De Rham cohomology of algebraic varieties, Publications Mathématiques I.H.E.S., 45 (1975), 1-99. | Numdam | MR | Zbl
,[19] Mathematische Werke, 2nd edition, Göttingen, Vandenhoeck & Ruprecht, 1970. | MR | Zbl
,[20] Sur les classes des corps circulaires, Journal de Math. pures et appliquées, 9e série, 11 (1932), 417-441. | JFM | Numdam
,[21] A remark on the rational points of abelian varieties with values in cyclotomic Zp-extensions, Proc. Japan Acad., 51 (1975), 12-16. | MR | Zbl
,[22] Lectures on p-adic L-functions, Princeton, Princeton University Press and University of Tokyo Press, 1972. | MR | Zbl
,[23] On p-adic L-functions, Ann. Math., 89 (1969), 198-205. | MR | Zbl
,[24] 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 | Zbl
,[25] Ueber gewisse Vereinfachungen der Transformationsgleichungen in der Theorie der elliptischen Functionen, Math. Ann., 37 (1890), 368-398. | JFM
,[26] On the congruences between Eisenstein series and cusp forms (to appear).
,[27] Universal bounds on the torsion of elliptic curves, Proc. London Math. Soc. (3), 33 (1976), 193-237. | MR | Zbl
,[28] Units in the modular function field, I, II, III, Math. Ann., 218 (1975), 67-96, 175-189, 273-285. | MR | Zbl
, ,[29] Elliptic Functions, Addison Wesley, Reading, 1974. | Zbl
,[30] 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
,[31] A uniform bound for p-torsion in elliptic curves [in Russian], Izv. Akad. Nauk. CCCP, 33 (1969), 459-465.
,[32] Parabolic points and zeta functions of modular forms [in Russian], Izv. Akad. Nauk. CCCP, 36 (1972), 19-65. | Zbl
,[33] Notes on étale cohomology of number fields, Ann. Scient. Éc. Norm. Sup., 4e série, t. 6 (1973), 521-556. | Numdam | MR | Zbl
,[34] Rational points on abelian varieties with values in towers of number fields, Inventiones Math., 18 (1972), 183-266. | MR | Zbl
,[35] Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, No. 414, Lecture Notes in Mathematics, No. 317, Berlin-Heidelberg-New York, Springer, 1973. | Numdam | MR | Zbl
,[36] 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
,[37] Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Mathematics, No. 370, Berlin-Heidelberg-New York, Springer, 1974. | MR | Zbl
, ,[38] 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
, ,[39] Arithmetic of Weil curves, Inventiones math., 25 (1974), 1-61. | MR | Zbl
, ,[40] Points of order 13 on elliptic curves, Inventiones math., 22 (1973), 41-49. | MR | Zbl
, ,[41] Courbes de Weil de conducteur 26, C. R. Acad. Sc. Paris, t. 275 (1972), série A, 743-745. | MR | Zbl
, ,[42] Elliptic curves of prime power conductor with Q-rational points of finite order, Osaka J Math., 10 (1973), 309-323. | MR | Zbl
,[43] Geometric invariant theory, Ergebnisse der Math., 34, Berlin-Heidelberg-New York, Springer, 1965. | MR | Zbl
,[44] Curves and their jacobians, Ann Arbor, The University of Michigan Press, 1975. | MR | Zbl
,[45] 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 | Zbl
,[46] Elliptische Kurven mit vorgeschriebenem Reduktionsverhalten, I, II, Math. Nachr., 49 (1971), 107-123; Math. Nachr., 56 (1973), 269-280. | Zbl
,[47] The first De Rham cohomology group and Dieudonné modules, Ann. scient. Éc. Norm. Sup., 4e série, t. 2 (1969), 63-135. | Numdam | MR | Zbl
,[48] Rational points on certain elliptic modular curves, Proc. Symp. Pure Math., 24 (1973), 221-231, A.M.S., Providence. | MR | Zbl
,[49] Diophantine equations and modular forms, Bull. A.M.S., 81 (1975), 14-27. | MR | Zbl
,[50] Hyperelliptic modular curves, Bull. Soc. Math. France, 102 (1974), 449-462. | Numdam | MR | Zbl
,[51] 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
,[52] On reductions and zeta functions of varieties obtained from Γo(N) (to appear).
,[53] Commutative group schemes, Lecture Notes in Mathematics, No. 15, Berlin-Heidelberg-New York, Springer, 1966. | MR | Zbl
,[54] Group schemes of prime order, Ann. Scient. Éc. Norm. Sup., série 4, 3 (1970), 1-21. | Numdam | MR | Zbl
, ,[55] Schémas en groupes de type (p, ...,p), Bull. Soc. Math. France, 102 (1974), 241-280. | Numdam | MR | Zbl
,[56] Spécialisation du foncteur de Picard, Publ. Math. I.H.E.S., 38 (1970), 27-76. | Numdam | MR | Zbl
,[57] 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 | Zbl
,[58] Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math., 101 (1975), 555-562. | MR | Zbl
,[59] Lie algebras of Galois groups arising from Hodge-Tate modules, Ann. of Math., 97 (1973), 160-170. | MR | Zbl
,[60] Corps locaux, Paris, Hermann, 1962. | MR | Zbl
,[61] 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
,[62] Algèbre locale. Multiplicités, Lecture Notes in Mathematics, No. 11 (3rd edition), Berlin-Heidelberg-New York, Springer, 1975. | MR | Zbl
,[63] Abelian l-adic representations and elliptic curves, Lectures at McGill University, New York-Amsterdam, W. A. Benjamin Inc., 1968. | MR | Zbl
,[64] Quelques propriétés des variétés abéliennes en caractéristique p, Amer. J. Math., 80 (1958), 715-739. | MR | Zbl
,[65] 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
,[66] 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
,[67] Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Inventiones math., 15 (1972), 259-331. | MR | Zbl
,[68] Elliptic curves of prime conductor, J. Lond. Math. Soc. (2), 10 (1975), 367-378. | MR | Zbl
,[69] Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Tokyo-Princeton, 1971. | Zbl
,[70] A table of Hecke operators, Proc. Japan Acad., 49 (1973), 380-384. | MR | Zbl
,[71] 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 | Zbl
,[72] Number theory, London-New York, Academic Press, 1966. | Zbl
, ,[73] A determination of the points which are rational over Q of three modular curves (unpublished). | Zbl
,[74] Good reduction of abelian varieties, Ann. of Math., 88 (1968), 492-517. | MR | Zbl
, ,[75] 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. and , Lecture Notes in Mathematics, Nos. 288, 340, Berlin-Heidelberg-New York, Springer, 1972, 1973. | Zbl