This page is about characterizing the Lazard ring in formal group laws. For the characterization of flat modules see instead at Lazard's criterion.
symmetric monoidal (∞,1)-category of spectra
algebraic topology – application of higher algebra and higher category theory to the study of (stable) homotopy theory
The Lazard ring is isomorphic to a graded polynomial ring
with the variable $t_i$ in degree $2 i$.
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
Frank Adams, part II.7 of Stable homotopy and generalised homology, 1974
Stanley Kochman, section 4.4 of Bordism, Stable Homotopy and Adams Spectral Sequences, AMS 1996
Mike Hopkins, Complex oriented cohomology theories and the language of stacks, 1999 course notes pdf
Akhil Mathew, Lazard’s theorem II, 2012
Jacob Lurie, Chromatic Homotopy Theory, Lecture series 2010, Lecture 2 Lazard’s theorem (pdf)
Jacob Lurie, Chromatic Homotopy Theory, Lecture series 2010, Lecture 3 Lazard’s theorem (continued) (pdf)
Dylan Wilson, Proof of Lazard’s theorem, lecture at 2013 Pre-Talbot Seminar, March 2013 (pdf)
Last revised on July 16, 2023 at 16:52:09. See the history of this page for a list of all contributions to it.