Reference request: Spec A_* is the automorphism group of the additive formal group law

Question

Dear all,

I'm seeking a reference for a claim made in lecture 8 of Jacob Lurie's chromatic homotopy theory notes (http://www.math.harvard.edu/~lurie/252xnotes/Lecture8.pdf). More particularly, Theorem 6 of this lecture states that (say over $\mathbb{F}_2$, so that things are commutative) the spectrum $\mathbb{G} = \operatorname{Spec} \mathcal{A}_*$ of the dual Steenrod algebra $\mathcal{A}_*$ is the automorphism group of the additive formal group law, in the obvious sense.

Lurie argues convincingly that $\mathbb{G}$ does act on the additive formal group law, but I don't think he attempts to prove that this action gives an isomorphism with the automorphism group. I'd be grateful if someone could give me a reference for this fact.

Cheers,

Saul

Answer 1

MIT OpenCourseWare has some notes from a course that Lurie taught in 2007. I believe the lecture on the dual Steenrod algebra has a proof of the claim.

Answer 2

If you're looking for a reference in print, it's in Ravenel's book Complex Cobordism and Stable Homotopy Groups of Spheres. See the comments after the proof of Theorem A2.2.18. (This book is available online, and you want Appendix 2.)