  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 closure of the field with p
elements and p is an odd prime. Using an adjunction between p-complete
nilpotent spaces and a subset of Hk-algebras, this paper shows that the unit of
this adjunction provides an isomorphism between these spectral sequences.
