A conceptual derivation of the dual Steenrod algebra

Abstract

In this note I give a conceptual proof of the fact that the mod 2 dual Steenrod algebra corepresents the group scheme of strict automorphisms of the formal additive group over \({\mathbb {F}}_2\). Contrary to existing proofs, it does not use the \(E_\infty \)-structure of \(H{\mathbb {F}}_2\) (Steenrod operations), nor does it proceed by producing a generators-and-relations presentation by some explicit calculation. Instead it relies on universal properties of bordism spectra, thus giving a stronger conceptual foundation for what is arguably the first instance of the well-studied deep connection between the algebraic geometry of formal groups and the stable homotopy category.