E∞ algebras and p-adic homotopy theory

Let Fp denote the field with p elements and F̄p its algebraic closure. We show that the singular cochain functor with coefficients in F̄p induces a contravariant equivalence between the homotopy category of connected p-complete nilpotent spaces of finite p-type and a full subcategory of the homotopy category of E∞F̄p-algebras.