nLab
Lazard's theorem

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Statement

Theorem

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 (Kochmann 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).

References

The proof is originally due to

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

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

Review includes

Last revised on July 6, 2016 at 11:17:31. See the history of this page for a list of all contributions to it.