Courbes modulaires de genre 1

Gerard Ligozat

Mémoires de la Société Mathématique de France (1975)

  • Volume: 43, page 5-80
  • ISSN: 0249-633X

How to cite

top

Ligozat, 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. [1] A. ATKIN et J. LEHNER — Hecke operators on Γo(m), Math. Ann., 185, 1970, pp. 134-160. Zbl0177.34901MR42 #3022
  2. [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. [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. [4] N. BOURBAKI — Variétés différentielles et analytiques, fascicule de résultats, § 10, Hermann, Paris 1971. 
  5. [5] J. CASSELS — Diophantine equations with special reference to elliptic curves, J. London Math. Soc., 41, 1966, pp. 193-291. Zbl0138.27002MR33 #7299
  6. [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. [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. [8] M.EICHLER — Quaternare quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion, Arch. Math., 5, 1954, pp. 355-366. Zbl0059.03804MR16,116d
  9. [9] R.FRICKE — Die elliptischen Funktionen und ihre Anwendungen, II, Teubner, Leipzig-Berlin, 1922. JFM48.0432.01
  10. [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. [11] E. HECKE — Mathematische Werke, Göttingen, Vandenhoeck und Ruprecht 1959. Zbl0092.00102MR21 #3303
  12. [12] J.IGUSA — Fibre systems of Jacobian varieties, III, Amer. J. of Math., 81, 1959, pp. 453-476. Zbl0115.38904MR21 #3422
  13. [13] J.IGUSA — Kroneckerian model of fields of elliptic modular functions, Amer. J. of Math., 81, 1959, pp. 561-577. Zbl0093.04502MR21 #7214
  14. [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. [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. [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. [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. [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. [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. [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. [21] A. NÉRON — Modèles minimaux et différentielles, C.I.M.E., 1969. 
  22. [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. [23] A.OGG — Elliptic curves and wild ramification, Amer. J. of Math., 89, 1967, pp. 1-21. Zbl0147.39803MR34 #7509
  24. [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. [25] A. OGG — Abelian curves of 2-power conductor, Proc. Cambr. Phil. Soc., 62, 1966, pp. 143-148. Zbl0163.15403MR34 #1320
  26. [26] A. OGG — Abelian curves of small conductor, Journ. reine u. angewandte Math., 226, 1968, pp. 204-215. Zbl0163.15404MR35 #1592
  27. [27] A. OGG — Dirichlet series and modular functions, Benjamin 1968. 
  28. [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. [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. [30] J.-P. SERRE et J.TATE — Good reduction of abelian varieties, Ann. of Math., 88, 1968, pp. 492-517. Zbl0172.46101MR38 #4488
  31. [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. [32] G. SHIMURA — Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, n° 11, Tokyo-Princeton, 1971. Zbl0221.10029
  33. [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. [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. [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. [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. [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. [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. [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. [40] A.WEIL — Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168, 1967, pp. 149-156. Zbl0158.08601MR34 #7473
  41. [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

top
  1. Galina V. Voskresenskaya, One special class of modular forms and group representations
  2. Marc Yor, Distributions de Frobénius
  3. B. Morlaye, Points rationnels sur 𝐐 de certaines courbes modulaires
  4. Philippe Revoy, Une classe d'équations cubiques
  5. Josep Gonzalez Rovira, Equations of hyperelliptic modular curves
  6. Fabien Pazuki, Remarques sur une conjecture de Lang
  7. Chad Schoen, On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.