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Let F _p denote the field with p elements and F ̄ _p its algebraic closure. We show that the singular cochain functor with coefficients in F ̄ _p 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 _∞F ̄ _p-algebras.