The focus of this paper is the comparison of two unstable homotopy spectral
sequences-- the unstable mod p Adams spectral sequence that computes the
unstable homotopy of a $p-$complete space, and the Goerss--Hopkins spectral
sequence, which computes the unstable homotopy of the space of E-infinity maps
between Hk-algebras, where k is the algebraic closer of the field with p
elements and p is an odd prime.