Isogenies and torsion of elliptic curves
Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 415-430.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we prove the uniform boundedness of the set of isogenies of certain classes of elliptic curves. The result obtained is applied to estimate the sum of exponents of torsion.
@article{IM2_1970_4_2_a8,
     author = {A. N. Parshin},
     title = {Isogenies and torsion of elliptic curves},
     journal = {Izvestiya. Mathematics },
     pages = {415--430},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a8/}
}
TY  - JOUR
AU  - A. N. Parshin
TI  - Isogenies and torsion of elliptic curves
JO  - Izvestiya. Mathematics 
PY  - 1970
SP  - 415
EP  - 430
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a8/
LA  - en
ID  - IM2_1970_4_2_a8
ER  - 
%0 Journal Article
%A A. N. Parshin
%T Isogenies and torsion of elliptic curves
%J Izvestiya. Mathematics 
%D 1970
%P 415-430
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a8/
%G en
%F IM2_1970_4_2_a8
A. N. Parshin. Isogenies and torsion of elliptic curves. Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 415-430. http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a8/

[1] Algebraicheskie poverkhnosti, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 75, 1965, 215 pp. | MR | Zbl

[2] Manin Yu. I., “$p$-kruchenie ellipticheskikh krivykh ravnomerno ogranicheno”, Izv. AN SSSR. Ser. matem., 33:3 (1969), 459–465 | MR

[3] Chebotarev N. G., Teoriya algebraicheskikh funktsii, Gostekhizdat, M., 1949

[4] Shafarevich I. R., “Polya algebraicheskikh chisel”, Proc. Internat. Congr. Math., Stockholm, 1962, 163–176

[5] Borel A., “Seminar on complex multiplication”, Lecture Notes in Mathem., 21, Springer, Berlin, 1966 | MR | Zbl

[6] Brieskorn E., “Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen”, Math. Ann., 166 (1966), 76–102 | DOI | MR | Zbl

[7] Cassels J., “Diophantine equations with special reference to elliptic curves”, J. London Math. Soc., 41 (1966), 193–291 | DOI | MR

[8] Fricke K., Die elliptischen Funktionen und ihre Anwendungen, v. 2, Teubner, Leipzig, 1922 | Zbl

[9] Gunning R. C., Lectures on modular forms, Notes by Armand Brumer. Annals of Mathematics Studies, 48, Princeton University Press, Princeton, N.J., 1962 | MR | Zbl

[10] Kodaira K., “On compact analytic surfaces. III”, Ann. Math., 78 (1963), 1–40 | DOI | MR | Zbl

[11] Mumford D., Geometric invariant theory, Springer, Berlin, 1965 | MR | Zbl

[12] Mumford D., “A remark on Mordell's conjecture”, Amer. J. Math., 87 (1965), 1007–1016 | DOI | MR | Zbl

[13] Neron A., “Modeles minimaux des varietes abeliennes sur les corps locaux et globaux”, Publ. Math. IHES, 1966, no. 21, 1–128 | MR

[14] Neron A., “Quasi-fonctions et hauteurs sur les varietes abeliennes”, Ann. Math., 82 (1965), 249–331 | DOI | MR | Zbl

[15] Raynoud M., “Modeles de Neron”, Compt. rend. Acad. sci., 162 (1966), 345–347 | MR

[16] Serre J.-P., Abelian $l$-adic representations and elliptic curves, Benjamin, New York, 1968 | MR | Zbl

[17] Serre J.-P., Cohomologie Galoisienne, Lecture Notes in Mathem., 5, Springer, Berlin, 1964

[18] Shimura G., “On the field of definition for a field of automorphic functions. II”, Ann. Math., 81 (1965), 124–165 | DOI | MR | Zbl