The Adams-Novikov \(E_2\)-term for computing \(\pi_*(L_2 V(0))\) at the prime 2 (Q1304854)

Let \(V(0)\) denote the mod \(p\) Moore spectrum, let \(E(2)\) stand for the corresponding Johnson-Wilson spectrum with coefficients \(E(2)_* \cong Z_{(p)}[v_1,v_2^{\pm 1}]\), and let \(L_2\) denote the Bousfield localization functor with respect to \(E(2)\). The \(E_2\)-term \(E_2^*(L_{2}V(0))\) of the Adams-Novikov spectral sequence converging to the homotopy groups of \(L_{2}V(0)\) is given by \(E_2^*(L_{2}V(0)) = \text{Ext}^*_{\Gamma}(A,A)\) over the Hopf algebroid \((A,\Gamma) = (E(2)_*, E(2)_*E(2))\). In the present paper the author determines the module structure of \(E_2^*(L_{2}V(0))\) for \(p=2\) using the chromatic spectral sequence.