There are many similarities between elliptic curves and formal groups of finite height. The points of order of a generic formal group are studied in order to develop the formal group analogue (applied to points of order ) of the concept of level structure and that of the -pairing known in elliptic curve theory.
Il y a beaucoup d’analogues entre les courbes elliptiques et les groupes formels de hauteur finie. Dans cet article on utilise les groupes formels génériques de Lubin-Tate pour développer pour les points d’ordre sur un groupe formel, les idées de structure de niveau et l’accouplement déjà connus dans la théorie des courbes elliptiques.
Zimmermann, Karl. Points of order $p$ of generic formal groups. Annales de l'Institut Fourier, Volume 38 (1988) no. 4, pp. 17-32. doi: 10.5802/aif.1148
@article{AIF_1988__38_4_17_0,
author = {Zimmermann, Karl},
title = {Points of order $p$ of generic formal groups},
journal = {Annales de l'Institut Fourier},
pages = {17--32},
year = {1988},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {38},
number = {4},
doi = {10.5802/aif.1148},
zbl = {0644.14016},
mrnumber = {90a:14065},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1148/}
}
TY - JOUR AU - Zimmermann, Karl TI - Points of order $p$ of generic formal groups JO - Annales de l'Institut Fourier PY - 1988 SP - 17 EP - 32 VL - 38 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1148/ DO - 10.5802/aif.1148 LA - en ID - AIF_1988__38_4_17_0 ER -
[1] , Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. | Zbl | MR
[2] , Geometric Algebra, Interscience Publishers, New York, 1957. | Zbl | MR
[3] , Elliptic modules, Math. USSR Sbornik, Vol. 23, N° 4, (1974), 561-592. | Zbl | MR
[4] and , Arithmetic Moduli of Eliptic Curves, Princeton University Press, New Jersey, 1985. | Zbl
[5] , Elliptic curves : Diophantine analysis, Springer Verlag 1978. | Zbl | MR
[6] , One parameter formal Lie groups over p-adic integer rings, Ann. of Math., 81 (1965), 380-387.
[7] and , Formal complex multiplication in local fields, Ann. of Math., 81 (1965), 380-387. | Zbl | MR
[8] and , Formal moduli for one parameter formal Lie group, Bull. Soc. Math. France, 94 (1966), 49-60. | Zbl | MR | Numdam
[9] , Canonical subgroups of formal groups, Trans. Amer. Math. Soc., 251 (1979), 103-127. | Zbl | MR
[10] , The local Kronecker-Weber Theorem, Trans. Amer. Math. Soc., 267 (1981), 133-138. | Zbl | MR
[11] , Local Rings, Interscience Publishers, New York, 1962. | Zbl | MR
Cited by Sources:
