ℎ₀-torsion bounds in the cohomology of the Steenrod algebra

Abstract

In this paper we use a technique of M. Hopkins to prove that the cohomology of the finite Hopf subalgebra of the mod 2 \bmod 2 Steenrod algebra generated by Sq ⁡ ( 2 i ) \operatorname {Sq}\left ( {{2^i}} \right ) with i ≤ n i \leq n , has h 0 {h_0} -torsion bound 2 n + 1 − n − 2  for  n ≥ 1 {2^{n + 1}} - n - 2{\text { for }}n \geq 1 .