nLab Lazard's theorem


This page is about characterizing the Lazard ring in formal group laws. For the characterization of flat modules see instead at Lazard's criterion.



Algebraic topology




The Lazard ring is isomorphic to a graded polynomial ring

L[t 1,t 2,] L \simeq \mathbb{Z}[t_1, t_2, \cdots]

with the variable t it_i in degree 2i2 i.

A proof is spelled out in (Kochman 96, theorem 4.4.9). Another proof is indicated in (Hopkins 99, section 2), worked out in (Mathew 12, Wilson 13). Also (Lurie 10, lecture 2, theorem 4) and (Lurie 10, lecture 3).


The proof is originally due to :

  • Michel Lazard, Sur les groupes de Lie Formels à un Paramètre, Bull. Soc. France 83 (1955) [numdam:BSMF_1955__83__251_0]

  • A. Fröhlich, Formal group, Lecture Notes in Mathematics 74, Springer (1968)

Review includes

Last revised on July 16, 2023 at 16:52:09. See the history of this page for a list of all contributions to it.