On subgroups of \(\pi_*(L_2T(1)\wedge M(2))\) at the prime two (Q1012427)

The Adams-Novikov spectral sequence is a tool that can be, in principle, used to determine the homotopy groups \(\pi_{*}(L_{2}T(1))\) where \(T(1)\) is the Ravenel spectrum and \(L_{2}\) denotes the Bousfield localization with respect to the \(\nu_{2}\)-localized Brown-Peterson spectrum \(\nu_{2}^{-1}BP\). This paper determines the \(s\)-th lines of the Adams-Novikov \(E_{\infty}\)-term for \(s = 0,1\) and \(s > 6\) of the Adams-Novikov spectral sequence converging to \(\pi_{*}(L_{2}T(1) \wedge M(2))\) where \(M(2)\) is the mod \(2^{2}\) Moore spectrum. The proofs are very technical and show just how disordered the \(E_{2}\)-term for \(\pi_{*}(L_2T(1))\) is.