Rational torsion points on elliptic curves over number fields
Séminaire Bourbaki (1993-1994)
- Volume: 36, page 209-227
- ISSN: 0303-1179
Access Full Article
topHow to cite
topEdixhoven, Bas. "Rational torsion points on elliptic curves over number fields." Séminaire Bourbaki 36 (1993-1994): 209-227. <http://eudml.org/doc/110184>.
@article{Edixhoven1993-1994,
author = {Edixhoven, Bas},
journal = {Séminaire Bourbaki},
keywords = {elliptic curve; order of the torsion part of the Mordell-Weil group; Jacobian; Eisenstein quotient},
language = {eng},
pages = {209-227},
publisher = {Société Mathématique de France},
title = {Rational torsion points on elliptic curves over number fields},
url = {http://eudml.org/doc/110184},
volume = {36},
year = {1993-1994},
}
TY - JOUR
AU - Edixhoven, Bas
TI - Rational torsion points on elliptic curves over number fields
JO - Séminaire Bourbaki
PY - 1993-1994
PB - Société Mathématique de France
VL - 36
SP - 209
EP - 227
LA - eng
KW - elliptic curve; order of the torsion part of the Mordell-Weil group; Jacobian; Eisenstein quotient
UR - http://eudml.org/doc/110184
ER -
References
top- [1] D. Abramovich. Formal finiteness and the uniform boundedness conjecture, a footnote to a paper of Kamienny and Mazur. Preprint March 1993. To appear in an Astérisque volume. MR1330925
- [2] P. Deligne, M. Rapoport. Les schémas de modules des courbes elliptiques. In Modular Functions of One Variable II. Springer Lecture Notes in Mathematics349 (1973). Zbl0281.14010MR337993
- [3] G. Faltings. The general case of S. Lang's conjecture. To appear in "The Barsotti symposium in algebraic geometry", W. Messing and V. Christante, eds. Acad. Press, Cambridge, Mass. Zbl0823.14009MR1307396
- [4] G. Frey. Links between solutions of A - B = C and elliptic curves. Number theory, Ulm 1987. Lecture Notes in Mathematics1380. Zbl0688.14018
- [5] G. Frey. A remark on isogenies of elliptic curves defined over quadratic fields. Compos. Math.58, 133-134 (1986). Zbl0596.14021MR834050
- [6] G. Frey. Curves with infinitely many points of fixed degree. Preprint, Institut für Experimentelle Mathematik (1992). Zbl0808.14022MR1264340
- [7] D. Bump, S. Friedberg and J. Hoffstein. Nonvanishing theorems for L-functions of modular forms and their derivatives. Invent. Math.102, 543-618 (1990). Zbl0721.11023MR1074487
- [8] S. Kamienny. Torsion points on elliptic curves and winding homomorphisms. MSRI preprint, December 1993. MR1058689
- [9] S. Kamienny, B. Mazur. Rational torsion of prime order in elliptic curves over number fields. To appear in an Astérisque volume. Zbl0846.14012MR1330929
- [10] N.M. Katz, B. Mazur. Arithmetic moduli of elliptic curves. Annals of Mathematics Studies108, Princeton University Press (1985). Zbl0576.14026MR772569
- [11] M. Kenku, F. Momose. Torsion points on elliptic curves defined over quadratic fields. Nagoya Mathematical Journal109, 125-149 (1988). Zbl0647.14020MR931956
- [12] V.A. Kolyvagin, D. Logachev. Finiteness of the Shafarevich-Tate group and group of rational points for some modular abelian varieties. Leningrad Math. J.1, 1229-1253 (1990). Zbl0728.14026MR1036843
- [13] D. Kubert. Universal bounds on the torsion of elliptic curves. Proceedings London Math. Soc. (3) 33, 193-237 (1976). Zbl0331.14010MR434947
- [14] J. Lehner, M. Newman. Weierstrass points of Γ0(N). Annals of Mathematics79, No. 2, 360-368 (1963). Zbl0124.29203
- [15] B. Levi. Sull'equazione indeterminata del 3° ordine. Atti del IV congresso internazionale dei matematici, Roma, 6-11 Aprile 1908, G. Castelnuovo editor. JFM40.0253.04
- [16] Y. Manin. A uniform bound for p-torsion in elliptic curves. Izv. Akad. Nauk. CCCP33, 459-465 (1969). Zbl0191.19601
- [17] B. Mazur. Modular curves and the Eisenstein ideal. Publications Mathématiques de l'IHES47, 33-186 (1977). Zbl0394.14008MR488287
- [18] B. Mazur. Rational isogenies of prime degree. Invent. Math.44, 129-162 (1978). Zbl0386.14009MR482230
- [19] B. Mazur and J-P.. Serre. Points rationnels des courbes modulaires X0(N). Séminaire Bourbaki exp.469 (1974-1975). Lecture Notes in Mathematics 514, 238-255 (1976). Zbl0346.14013MR485882
- [20] L. Merel. Bornes pour la torsion des courbes elliptiques sur les corps de nombres. To appear. Zbl0936.11037MR1369424
- [21] M.R. Murty and V.K. Murty. Mean values of derivatives of modular L-series. Ann. Math.133, 447-475 (1991). Zbl0745.11032MR1109350
- [22] A. Ogg. Rational points of finite order on elliptic curves. Invent. Math.12, 105-111 (1971). Zbl0216.05602MR291084
- [23] J-P. Serre. p-torsion des courbes elliptiques (d'après Y. Manin). Séminaire Bourbaki exp.380 (1969-1970). Lecture Notes in Mathematics 180, 281-294 (1971). Zbl0222.14019
- [24] A. Silverberg. Points of finite order on abelian varieties. Contemporary Mathematics133, 175-193 (1992). Zbl0787.14028MR1183978
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.