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 $${\mathbb {F}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> . Contrary to existing proofs, it does not use the $$E_\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> -structure of $$H{\mathbb {F}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> (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.