The Adams-Novikov $E_2$-term for $\pi_*(L_2S^0)$ at the prime 2

Abstract.

In this paper we determine the $E_2$-term of the Adams-Novikov spectral sequence converging to the homotopy groups $\pi_*(L_2S^0)$ of $L_2$-localized sphere spectrum at the prime 2. The structure of the $E_2$-term indicates that the homotopy group $\pi_i(L_2S^0)$ is finite except for i=0,-4 and -5.