Courbes modulaires de genre 1
Mémoires de la Société Mathématique de France (1975)
- Volume: 43, page 5-80
- ISSN: 0249-633X
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topLigozat, Gerard. "Courbes modulaires de genre 1." Mémoires de la Société Mathématique de France 43 (1975): 5-80. <http://eudml.org/doc/94716>.
@article{Ligozat1975,
author = {Ligozat, Gerard},
journal = {Mémoires de la Société Mathématique de France},
language = {fre},
pages = {5-80},
publisher = {Société mathématique de France},
title = {Courbes modulaires de genre 1},
url = {http://eudml.org/doc/94716},
volume = {43},
year = {1975},
}
TY - JOUR
AU - Ligozat, Gerard
TI - Courbes modulaires de genre 1
JO - Mémoires de la Société Mathématique de France
PY - 1975
PB - Société mathématique de France
VL - 43
SP - 5
EP - 80
LA - fre
UR - http://eudml.org/doc/94716
ER -
References
top- [1] A. ATKIN et J. LEHNER — Hecke operators on Γo(m), Math. Ann., 185, 1970, pp. 134-160. Zbl0177.34901MR42 #3022
- [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. Zbl0118.27601MR26 #3669
- [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. Zbl0147.02506MR31 #3419
- [4] N. BOURBAKI — Variétés différentielles et analytiques, fascicule de résultats, § 10, Hermann, Paris 1971.
- [5] J. CASSELS — Diophantine equations with special reference to elliptic curves, J. London Math. Soc., 41, 1966, pp. 193-291. Zbl0138.27002MR33 #7299
- [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. Zbl0281.14010MR49 #2762
- [7] K.DOI — On the jacobian varieties of the fields of elliptic modular functions, Osaka Math. J., 15, 1963, pp. 249-256. Zbl0141.18301MR32 #5655
- [8] M.EICHLER — Quaternare quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion, Arch. Math., 5, 1954, pp. 355-366. Zbl0059.03804MR16,116d
- [9] R.FRICKE — Die elliptischen Funktionen und ihre Anwendungen, II, Teubner, Leipzig-Berlin, 1922. JFM48.0432.01
- [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. Zbl0248.14006MR50 #7134
- [11] E. HECKE — Mathematische Werke, Göttingen, Vandenhoeck und Ruprecht 1959. Zbl0092.00102MR21 #3303
- [12] J.IGUSA — Fibre systems of Jacobian varieties, III, Amer. J. of Math., 81, 1959, pp. 453-476. Zbl0115.38904MR21 #3422
- [13] J.IGUSA — Kroneckerian model of fields of elliptic modular functions, Amer. J. of Math., 81, 1959, pp. 561-577. Zbl0093.04502MR21 #7214
- [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° 6, 1971, pp. 7-78]. Zbl0266.14012
- [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]. Zbl0248.14010
- [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. Zbl0141.18302MR32 #5656
- [17] B.MAZUR — Rational Points of Abelian Varieties with Values in Towers of Number Fields, Invent. Math., 18, 1972, pp. 183-266. Zbl0245.14015MR56 #3020
- [18] B.MAZUR — Courbes elliptiques et symboles modulaires, Sém. Bourbaki, 24e année, 1971/1972, exposé n° 414, Lecture Notes in Math., 317, Berlin-Heidelberg New York, Springer 1973. Zbl0276.14012
- [19] B.MAZUR et J. VÉLU — Courbes de Weil de conducteur 26, C.R. Acad. Sci. Paris, 275, 1972, pp. 743-745. Zbl0241.14015MR47 #8551
- [20] A.NÉRON — Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. I.H.E.S., 21, 1964. Zbl0132.41403MR31 #3423
- [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. Zbl0178.43001MR21 #6354
- [23] A.OGG — Elliptic curves and wild ramification, Amer. J. of Math., 89, 1967, pp. 1-21. Zbl0147.39803MR34 #7509
- [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. Zbl0258.10012MR49 #2554
- [25] A. OGG — Abelian curves of 2-power conductor, Proc. Cambr. Phil. Soc., 62, 1966, pp. 143-148. Zbl0163.15403MR34 #1320
- [26] A. OGG — Abelian curves of small conductor, Journ. reine u. angewandte Math., 226, 1968, pp. 204-215. Zbl0163.15404MR35 #1592
- [27] A. OGG — Dirichlet series and modular functions, Benjamin 1968.
- [28] J.-P. SERRE — Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15, 1972, pp. 259-331. Zbl0235.14012MR52 #8126
- [29] J.-P. SERRE — Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures), Sém. Delange-Pisot-Poitou, 1969/1970, n° 19). Zbl0214.48403
- [30] J.-P. SERRE et J.TATE — Good reduction of abelian varieties, Ann. of Math., 88, 1968, pp. 492-517. Zbl0172.46101MR38 #4488
- [31] G. SHIMURA — Correspondances modulaires et les fonctions ζ de courbes algébriques, J. Math. Soc. Japan, 10, n° 1, 1958, pp. 1-28. Zbl0081.07603MR20 #1679
- [32] G. SHIMURA — Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, n° 11, Tokyo-Princeton, 1971. Zbl0221.10029
- [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. Zbl0221.10023MR37 #5225
- [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. MR36 #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. Zbl0197.47101MR37 #6287
- [36] J. TATE — Algorithm for determining the type of a singular fibre in an elliptic pencil (notes diffusées par l'I.H.E.S.). Zbl1214.14020
- [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° 306, 1965/1966, New York-Amsterdam, Benjamin 1966. Zbl0199.55604
- [39] J. VÉLU — Courbes elliptiques sur 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. Zbl0225.14013
- [40] A.WEIL — Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168, 1967, pp. 149-156. Zbl0158.08601MR34 #7473
- [41] G. SANSONE et J. CASSELS — Sur le problème de M.Werner Mnich, Acta Arithmetica, 7, 1961/1962, pp. 187-190. Zbl0100.27403MR24 #A2550
Citations in EuDML Documents
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- Marc Yor, Distributions de Frobénius
- B. Morlaye, Points rationnels sur de certaines courbes modulaires
- Philippe Revoy, Une classe d'équations cubiques
- Josep Gonzalez Rovira, Equations of hyperelliptic modular curves
- Fabien Pazuki, Remarques sur une conjecture de Lang
- Chad Schoen, On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field
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