Rational torsion points on elliptic curves over number fields

Edixhoven, Bas

Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 782, 19 p.

@incollection{SB_1993-1994__36__209_0,
     author = {Edixhoven, Bas},
     title = {Rational torsion points on elliptic curves over number fields},
     booktitle = {S\'eminaire Bourbaki : volume 1993/94, expos\'es 775-789},
     series = {Ast\'erisque},
     note = {talk:782},
     pages = {209--227},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {227},
     year = {1995},
     mrnumber = {1321648},
     zbl = {0832.14024},
     language = {en},
     url = {http://www.numdam.org/item/SB_1993-1994__36__209_0/}
}

TY  - CHAP
AU  - Edixhoven, Bas
TI  - Rational torsion points on elliptic curves over number fields
BT  - Séminaire Bourbaki : volume 1993/94, exposés 775-789
AU  - Collectif
T3  - Astérisque
N1  - talk:782
PY  - 1995
SP  - 209
EP  - 227
IS  - 227
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_1993-1994__36__209_0/
LA  - en
ID  - SB_1993-1994__36__209_0
ER  -

%0 Book Section
%A Edixhoven, Bas
%T Rational torsion points on elliptic curves over number fields
%B Séminaire Bourbaki : volume 1993/94, exposés 775-789
%A Collectif
%S Astérisque
%Z talk:782
%D 1995
%P 209-227
%N 227
%I Société mathématique de France
%U http://www.numdam.org/item/SB_1993-1994__36__209_0/
%G en
%F SB_1993-1994__36__209_0

Edixhoven, Bas. Rational torsion points on elliptic curves over number fields, dans Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 782, 19 p. http://www.numdam.org/item/SB_1993-1994__36__209_0/

Bibliographie
Cité par

[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. | MR

[2] P. Deligne, M. Rapoport. Les schémas de modules des courbes elliptiques. In Modular Functions of One Variable II. Springer Lecture Notes in Mathematics 349 (1973). | MR | Zbl

[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. | MR | Zbl

[4] G. Frey. Links between solutions of $A - B = C$ and elliptic curves. Number theory, Ulm 1987. Lecture Notes in Mathematics 1380. | Zbl

[5] G. Frey. A remark on isogenies of elliptic curves defined over quadratic fields. Compos. Math. 58, 133-134 (1986). | EuDML | Numdam | MR | Zbl

[6] G. Frey. Curves with infinitely many points of fixed degree. Preprint, Institut für Experimentelle Mathematik (1992). | MR | Zbl

[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). | DOI | EuDML | MR | Zbl

[8] S. Kamienny. Torsion points on elliptic curves and winding homomorphisms. MSRI preprint, December 1993. | MR | Zbl

[9] S. Kamienny, B. Mazur. Rational torsion of prime order in elliptic curves over number fields. To appear in an Astérisque volume. | Numdam | MR | Zbl

[10] N. M. Katz, B. Mazur. Arithmetic moduli of elliptic curves. Annals of Mathematics Studies 108, Princeton University Press (1985). | MR | Zbl

[11] M. Kenku, F. Momose. Torsion points on elliptic curves defined over quadratic fields. Nagoya Mathematical Journal 109, 125-149 (1988). | DOI | MR | Zbl

[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). | MR | Zbl

[13] D. Kubert. Universal bounds on the torsion of elliptic curves. Proceedings London Math. Soc. (3) 33, 193-237 (1976). | DOI | MR | Zbl

[14] J. Lehner, M. Newman. Weierstrass points of $Γ_{0} (N)$ . Annals of Mathematics 79, No. 2, 360-368 (1963). | DOI | Zbl

[15] B. Levi. Sull'equazione indeterminata del 3° ordine. Atti del IV congresso internazionale dei matematici, Roma, 6-11 Aprile 1908, G. Castelnuovo editor. | JFM

[16] Y. Manin. A uniform bound for $p$ -torsion in elliptic curves. Izv. Akad. Nauk. CCCP 33, 459-465 (1969). | Zbl

[17] B. Mazur. Modular curves and the Eisenstein ideal. Publications Mathématiques de l'IHES 47, 33-186 (1977). | DOI | EuDML | Numdam | MR | Zbl

[18] B. Mazur. Rational isogenies of prime degree. Invent. Math. 44, 129-162 (1978). | DOI | EuDML | MR | Zbl

[19] B. Mazur and J-P.. Serre. Points rationnels des courbes modulaires $X_{0} (N)$ . Séminaire Bourbaki exp. 469 (1974-1975). Lecture Notes in Mathematics 514, 238-255 (1976). | EuDML | Numdam | MR | Zbl

[20] L. Merel. Bornes pour la torsion des courbes elliptiques sur les corps de nombres. To appear. | DOI | MR | Zbl

[21] M. R. Murty and V. K. Murty. Mean values of derivatives of modular $L$ -series. Ann. Math. 133, 447-475 (1991). | DOI | MR | Zbl

[22] A. Ogg. Rational points of finite order on elliptic curves. Invent. Math. 12, 105-111 (1971). | DOI | EuDML | MR | Zbl

[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). | EuDML | Numdam | Zbl

[24] A. Silverberg. Points of finite order on abelian varieties. Contemporary Mathematics 133, 175-193 (1992). | DOI | MR | Zbl