An embedding for the \(E_{2}\)-term of the Adams spectral sequence at odd primes
In an earlier paper [Ricerche Mat., to appear] the first and third author studied an algebra homomorphism \(\overline{\pi}:Q_1 \to {\mathcal A}\), where \({\mathcal A}\) denotes the mod \(2\) Steenrod algebra, and showed that the induced homomorphism \(\text{Ext}_{\mathcal A}({\mathbb F}_2,{\mathbb F}_2) \to \text{Ext}_{Q_1}({\mathbb F}_2,{\mathbb F}_2)\) was injective. Hence the \(E_2\)-term of the Adams spectral sequence is displayed as a subalgebra of this latter Ext group. The algebra \(Q_1\) is related to the algebra \(Q\) of cohomology operations in the category of \(H_{\infty}\)-ring spectra, as studied by \textit{J. P. May} [Steenrod Algebra Appl., Lect. Notes Math. 168, 153--231 (1970; Zbl 0242.55023)], by a change of Koszul generators. In the paper under review the authors carry out the analogous programme for odd primes. They also offer a more specific relation between the two Ext groups under the assumption that \(Q\) is Koszul. It is not yet clear that this assumption holds but the authors offer some evidence for it.
scientific article; zbMATH DE number 5156860
scientific article