The Lazard ring is a commutative ring which is
and by Quillen's theorem also
The Lazard ring may be presented by generators with
and relations as follows
the obvious associativity relation
the universal 1-dimensional formal group law is the formal power series
in two variables with coefficients in the Lazard ring.
review includes (Hopkins 99, theorem 2.3, theorem 2.5)
Passing to formal dual ring spectra, this says that is something like the moduli space for formal groups. By Quillen's theorem on MU, the lift of to higher algebra is the E-infinity ring MU and the E-infinity ring spectrum is something like the derived moduli stack for formal group laws.
Lazard's theorem states:
Let denote the peridodic complex cobordism cohomology theory. Its cohomology ring over the point together with its formal group law is naturally isomorphic to the universal Lazard ring with its formal group law .
for any . This construction could however break the left exactness condition. However, built this way will be left exact if the ring morphism is a flat morphism. This is the Landweber exactness condition (or maybe slightly stronger). See at Landweber exact functor theorem.
for some context see A Survey of Elliptic Cohomology - cohomology theories
Stanley Kochmann, section 4.4 of Bordism, Stable Homotopy and Adams Spectral Sequences, AMS 1996