Reference request: Spec A_* is the automorphism group of the additive formal group law - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T09:07:42Z http://mathoverflow.net/feeds/question/73675 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/73675/reference-request-spec-a-is-the-automorphism-group-of-the-additive-formal-grou Reference request: Spec A_* is the automorphism group of the additive formal group law Saul Glasman 2011-08-25T17:20:30Z 2011-08-25T18:59:03Z <p>Dear all,</p> <p>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 <code>$\mathbb{F}_2$</code>, so that things are commutative) the spectrum <code>$\mathbb{G} = \operatorname{Spec} \mathcal{A}_*$</code> of the dual Steenrod algebra $\mathcal{A}_*$ is the automorphism group of the additive formal group law, in the obvious sense.</p> <p>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.</p> <p>Cheers,</p> <p>Saul</p> http://mathoverflow.net/questions/73675/reference-request-spec-a-is-the-automorphism-group-of-the-additive-formal-grou/73677#73677 Answer by S. Carnahan for Reference request: Spec A_* is the automorphism group of the additive formal group law S. Carnahan 2011-08-25T17:32:54Z 2011-08-25T17:32:54Z <p>MIT OpenCourseWare has some <a href="http://ocw.mit.edu/courses/mathematics/18-917-topics-in-algebraic-topology-the-sullivan-conjecture-fall-2007/lecture-notes/" rel="nofollow">notes from a course</a> that Lurie taught in 2007. I believe <a href="http://ocw.mit.edu/courses/mathematics/18-917-topics-in-algebraic-topology-the-sullivan-conjecture-fall-2007/lecture-notes/lecture13.pdf" rel="nofollow">the lecture on the dual Steenrod algebra</a> has a proof of the claim.</p> http://mathoverflow.net/questions/73675/reference-request-spec-a-is-the-automorphism-group-of-the-additive-formal-grou/73693#73693 Answer by John Palmieri for Reference request: Spec A_* is the automorphism group of the additive formal group law John Palmieri 2011-08-25T18:59:03Z 2011-08-25T18:59:03Z <p>If you're looking for a reference in print, it's in Ravenel's book <em>Complex Cobordism and Stable Homotopy Groups of Spheres</em>. See the comments after the proof of Theorem A2.2.18. (This book is <a href="http://www.math.rochester.edu/people/faculty/doug/mu.html#repub" rel="nofollow">available online</a>, and you want Appendix 2.)</p>