×

zbMATH — the first resource for mathematics

Courbes modulaires de genre 1. (French) Zbl 0322.14011

MSC:
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14H25 Arithmetic ground fields for curves
14G05 Rational points
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] A. ATKIN et J. LEHNER - Hecke operators on \Gamma o(m) , Math. Ann., 185, 1970 , pp. 134-160. MR 42 #3022 | Zbl 0177.34901 · Zbl 0177.34901 · doi:10.1007/BF01359701 · eudml:161948
[2] B.J.BIRCH et H.P.F. SWINNERTON-DYER - Notes on elliptic curves. I , Journ. reine u. angewandte Math., 212, 1963 , pp. 7-25. Article | MR 26 #3669 | Zbl 0118.27601 · Zbl 0118.27601 · doi:10.1515/crll.1963.212.7 · crelle:GDZPPN002180022 · eudml:150565
[3] B.J. BIRCH et H.P.F. SWINNERTON-DYER - Notes on elliptic curves , II, Journ. reine u. angewandte Math., 218, 1965 , pp. 79-108. Article | MR 31 #3419 | Zbl 0147.02506 · Zbl 0147.02506 · doi:10.1515/crll.1965.218.79 · crelle:GDZPPN002181169 · eudml:150676
[4] N. BOURBAKI - Variétés différentielles et analytiques , fascicule de résultats, 10, Hermann, Paris 1971 . · Zbl 0206.50402
[5] J. CASSELS - Diophantine equations with special reference to elliptic curves , J. London Math. Soc., 41, 1966 , pp. 193-291. MR 33 #7299 | Zbl 0138.27002 · Zbl 0138.27002 · doi:10.1112/jlms/s1-41.1.193
[6] P.DELIGNE et M.RAPOPORT - Les schémas de modules de courbes elliptiques , Modular Functions of one Variable II, Lecture Notes in Math. 349, pp. 143-316, Berlin-Heidelberg-New York, Springer 1973 . MR 49 #2762 | Zbl 0281.14010 · Zbl 0281.14010
[7] K.DOI - On the jacobian varieties of the fields of elliptic modular functions , Osaka Math. J., 15, 1963 , pp. 249-256. MR 32 #5655 | Zbl 0141.18301 · Zbl 0141.18301
[8] M.EICHLER - Quaternare quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion , Arch. Math., 5, 1954 , pp. 355-366. MR 16,116d | Zbl 0059.03804 · Zbl 0059.03804 · doi:10.1007/BF01898377
[9] R.FRICKE - Die elliptischen Funktionen und ihre Anwendungen , II, Teubner, Leipzig-Berlin, 1922 . JFM 48.0432.01 · JFM 48.0432.01
[10] A.GROTHENDIECK - Modèles de Néron et monodromie , Groupes de monodromie en Géométrie Algébrique (SGA 7 I), Exposé IX, Lecture Notes in Math., 288, pp. 313-523, Berlin-Heidelberg-New York, Springer 1972 . MR 50 #7134 | Zbl 0248.14006 · Zbl 0248.14006
[11] E. HECKE - Mathematische Werke , Göttingen, Vandenhoeck und Ruprecht 1959 . MR 21 #3303 | Zbl 0092.00102 · Zbl 0092.00102
[12] J.IGUSA - Fibre systems of Jacobian varieties , III, Amer. J. of Math., 81, 1959 , pp. 453-476. MR 21 #3422 | Zbl 0115.38904 · Zbl 0115.38904 · doi:10.2307/2372751
[13] J.IGUSA - Kroneckerian model of fields of elliptic modular functions , Amer. J. of Math., 81, 1959 , pp. 561-577. MR 21 #7214 | Zbl 0093.04502 · Zbl 0093.04502 · doi:10.2307/2372914
[14] Y.MANIN - Corps cyclotomiques et courbes modulaires (en russe) , Uspekhi Mat. Nauk. Tom XXVI 6 (161), 1971 , pp. 7-71 [trad. anglaise : Russian Math. Surveys, vol. 26, n^\circ 6, 1971 , pp. 7-78]. Zbl 0266.14012 · Zbl 0266.14012 · doi:10.1070/rm1971v026n06ABEH001272
[15] Y.MANIN - Points paraboliques et fonctions zêta des courbes modulaires (en russe) , Izv. Akad. N. C.C.C.P., 36, 1972 , pp. 19-66 [trad. anglaise : Math. USSR-Izvestja, 6, 1972 , pp. 19-64]. Zbl 0248.14010 · Zbl 0248.14010 · doi:10.1070/IM1972v006n01ABEH001867
[16] T.MATSUI - On the endomorphism algebra of Jacobian varieties attached to the fields of elliptic modular functions , Osaka J. Math., 1, 1964 , pp. 25-31. MR 32 #5656 | Zbl 0141.18302 · Zbl 0141.18302
[17] B.MAZUR - Rational Points of Abelian Varieties with Values in Towers of Number Fields , Invent. Math., 18, 1972 , pp. 183-266. MR 56 #3020 | Zbl 0245.14015 · Zbl 0245.14015 · doi:10.1007/BF01389815 · eudml:142180
[18] B.MAZUR - Courbes elliptiques et symboles modulaires , Sém. Bourbaki, 24e année, 1971 / 1972 , exposé n^\circ 414, Lecture Notes in Math., 317, Berlin-Heidelberg New York, Springer 1973 . Numdam | Zbl 0276.14012 · Zbl 0276.14012 · numdam:SB_1971-1972__14__277_0 · eudml:109817
[19] B.MAZUR et J. VÉLU - Courbes de Weil de conducteur 26 , C.R. Acad. Sci. Paris, 275, 1972 , pp. 743-745. MR 47 #8551 | Zbl 0241.14015 · Zbl 0241.14015
[20] A.NÉRON - Modèles minimaux des variétés abéliennes sur les corps locaux et globaux , Publ. Math. I.H.E.S., 21, 1964 . Numdam | MR 31 #3423 | Zbl 0132.41403 · Zbl 0132.41403 · doi:10.1007/BF02684271 · numdam:PMIHES_1964__21__5_0 · eudml:103844
[21] A. NÉRON - Modèles minimaux et différentielles , C.I.M.E., 1969 .
[22] M.NEWMAN - Construction and application of a class of modular functions , Proc. London Math., Soc., (3) 7, 1957 , pp. 334-350 ; Construction and application of a class of modular functions II, ibid., (3) 9, 1959 , pp. 373-387. MR 21 #6354 | Zbl 0178.43001 · Zbl 0178.43001 · doi:10.1112/plms/s3-9.3.373
[23] A.OGG - Elliptic curves and wild ramification , Amer. J. of Math., 89, 1967 , pp. 1-21. MR 34 #7509 | Zbl 0147.39803 · Zbl 0147.39803 · doi:10.2307/2373092
[24] A.OGG - Survey of Modular Functions of one Variable , Modular Functions of one Variable I, Lecture Notes in Math. 320, pp. 1-35, Berlin-Heidelberg-New York, Springer 1973 . MR 49 #2554 | Zbl 0258.10012 · Zbl 0258.10012
[25] A. OGG - Abelian curves of 2-power conductor , Proc. Cambr. Phil. Soc., 62, 1966 , pp. 143-148. MR 34 #1320 | Zbl 0163.15403 · Zbl 0163.15403
[26] A. OGG - Abelian curves of small conductor , Journ. reine u. angewandte Math., 226, 1968 , pp. 204-215. Article | MR 35 #1592 | Zbl 0163.15404 · Zbl 0163.15404 · doi:10.1515/crll.1967.226.204 · crelle:GDZPPN002182394 · eudml:150797
[27] A. OGG - Dirichlet series and modular functions , Benjamin 1968 . · Zbl 0191.38101
[28] J.-P. SERRE - Propriétés galoisiennes des points d’ordre fini des courbes elliptiques , Invent. Math., 15, 1972 , pp. 259-331. MR 52 #8126 | Zbl 0235.14012 · Zbl 0235.14012 · doi:10.1007/BF01405086 · eudml:142133
[29] J.-P. SERRE - Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures) , Sém. Delange-Pisot-Poitou, 1969 / 1970 , n^\circ 19). Numdam | Zbl 0214.48403 · Zbl 0214.48403 · numdam:SDPP_1969-1970__11_2_A4_0 · eudml:110758
[30] J.-P. SERRE et J.TATE - Good reduction of abelian varieties , Ann. of Math., 88, 1968 , pp. 492-517. MR 38 #4488 | Zbl 0172.46101 · Zbl 0172.46101 · doi:10.2307/1970722
[31] G. SHIMURA - Correspondances modulaires et les fonctions \zeta de courbes algébriques , J. Math. Soc. Japan, 10, n^\circ 1, 1958 , pp. 1-28. Article | MR 20 #1679 | Zbl 0081.07603 · Zbl 0081.07603 · doi:10.2969/jmsj/01010001 · minidml.mathdoc.fr
[32] G. SHIMURA - Introduction to the arithmetic theory of automorphic functions , Publ. Math. Soc. Japan, n^\circ 11, Tokyo-Princeton, 1971 . Zbl 0221.10029 · Zbl 0221.10029
[33] N.M. STEPHENS - The diophantine equation X3 + Y3 = DZ3 and the conjectures of Birch and Swinnerton-Dyer , J. reine u. angewandte Math., 231, 1968 , pp. 121-162. Article | MR 37 #5225 | Zbl 0221.10023 · Zbl 0221.10023 · doi:10.1515/crll.1968.231.121 · crelle:GDZPPN002183072 · eudml:150864
[34] P. SWINNERTON-DYER - An Application of Computing to Class Field Theory , dans : J. CASSELS et A. FRÖHLICH (ed.) : Algebraic Number Theory, pp. 280-291, London-New York, Academic Press 1967 . MR 36 #2595
[35] P. SWINNERTON-DYER - The Conjectures of Birch and Swinnerton-Dyer , and of Tate, Proceedings of a Conference on Local Fields, NUFFIC Summer School held at Driebergen, pp. 132-157, 1966 , Berlin-Heidelberg-New York, Springer 1967 . MR 37 #6287 | Zbl 0197.47101 · Zbl 0197.47101
[36] J. TATE - Algorithm for determining the type of a singular fibre in an elliptic pencil (notes diffusées par l’I.H.E.S.) .
[37] J. TATE - Rational points on elliptic curves , course given at Haverford (May, April 1961 ), re-edited, 1970 , without the author’s permission by ”Faculté des Sciences de Poitiers”.
[38] J. TATE - On the conjectures of Birch and Swinnerton-Dyer and a geometric analog ., Sém. Bourbaki, exp. n^\circ 306, 1965 / 1966 , New York-Amsterdam, Benjamin 1966 . Numdam | Zbl 0199.55604 · Zbl 0199.55604 · numdam:SB_1964-1966__9__415_0 · eudml:109707
[39] J. VÉLU - Courbes elliptiques sur \Bbb Q ayant bonne réduction en dehors de {11} , C.R. Acad. Sci. Paris, 273, 1971 , pp. 73-75 ; Isogénies entre courbes elliptiques ibid., 273, 1971 , pp. 238-241. Zbl 0225.14013 · Zbl 0225.14013
[40] A.WEIL - Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen , Math. Ann., 168, 1967 , pp. 149-156. MR 34 #7473 | Zbl 0158.08601 · Zbl 0158.08601 · doi:10.1007/BF01361551 · eudml:161499
[41] G. SANSONE et J. CASSELS - Sur le problème de M.Werner Mnich , Acta Arithmetica, 7, 1961 / 1962 , pp. 187-190. Article | MR 24 #A2550 | Zbl 0100.27403 · Zbl 0100.27403 · eudml:206999
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.