Points of order p of generic formal groups

Karl Zimmermann

Annales de l'institut Fourier (1988)

  • Volume: 38, Issue: 4, page 17-32
  • ISSN: 0373-0956

Abstract

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There are many similarities between elliptic curves and formal groups of finite height. The points of order p of a generic formal group are studied in order to develop the formal group analogue (applied to points of order p ) of the concept of level structure and that of the e n -pairing known in elliptic curve theory.

How to cite

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Zimmermann, Karl. "Points of order $p$ of generic formal groups." Annales de l'institut Fourier 38.4 (1988): 17-32. <http://eudml.org/doc/74814>.

@article{Zimmermann1988,
abstract = {There are many similarities between elliptic curves and formal groups of finite height. The points of order $p$ of a generic formal group are studied in order to develop the formal group analogue (applied to points of order $p$) of the concept of level structure and that of the $e_n$-pairing known in elliptic curve theory.},
author = {Zimmermann, Karl},
journal = {Annales de l'institut Fourier},
keywords = {points of order p of a generic formal group; level structure; elliptic curve},
language = {eng},
number = {4},
pages = {17-32},
publisher = {Association des Annales de l'Institut Fourier},
title = {Points of order $p$ of generic formal groups},
url = {http://eudml.org/doc/74814},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Zimmermann, Karl
TI - Points of order $p$ of generic formal groups
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 4
SP - 17
EP - 32
AB - There are many similarities between elliptic curves and formal groups of finite height. The points of order $p$ of a generic formal group are studied in order to develop the formal group analogue (applied to points of order $p$) of the concept of level structure and that of the $e_n$-pairing known in elliptic curve theory.
LA - eng
KW - points of order p of a generic formal group; level structure; elliptic curve
UR - http://eudml.org/doc/74814
ER -

References

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  1. [1] E. ARTIN, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. Zbl0194.35301MR38 #5742
  2. [2] E. ARTIN, Geometric Algebra, Interscience Publishers, New York, 1957. Zbl0077.02101MR18,553e
  3. [3] V. G. DRINFEL'D, Elliptic modules, Math. USSR Sbornik, Vol. 23, N° 4, (1974), 561-592. Zbl0321.14014MR52 #5580
  4. [4] N. KATZ and B. MAZUR, Arithmetic Moduli of Eliptic Curves, Princeton University Press, New Jersey, 1985. Zbl0576.14026
  5. [5] S. LANG, Elliptic curves : Diophantine analysis, Springer Verlag 1978. Zbl0388.10001MR81b:10009
  6. [6] J. LUBIN, One parameter formal Lie groups over p-adic integer rings, Ann. of Math., 81 (1965), 380-387. Zbl0128.26501
  7. [7] J. LUBIN and J. TATE, Formal complex multiplication in local fields, Ann. of Math., 81 (1965), 380-387. Zbl0128.26501MR30 #3094
  8. [8] J. LUBIN and J. TATE, Formal moduli for one parameter formal Lie group, Bull. Soc. Math. France, 94 (1966), 49-60. Zbl0156.04105MR39 #214
  9. [9] J. LUBIN, Canonical subgroups of formal groups, Trans. Amer. Math. Soc., 251 (1979), 103-127. Zbl0431.14014MR80j:14039
  10. [10] J. LUBIN, The local Kronecker-Weber Theorem, Trans. Amer. Math. Soc., 267 (1981), 133-138. Zbl0476.12014MR82i:12017
  11. [11] M. NAGATA, Local Rings, Interscience Publishers, New York, 1962. Zbl0123.03402MR27 #5790

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