E-infinity algebras and p-adic homotopy theory

Let F-p denote the field with p elements and (F) over bar (p) its algebraic closure. We show that the singular cochain functor with coefficients in (F ) over bar (p) induces a contravariant equivalence between the homotopy cat egory of connected p-complete nilpotent spaces of finite p-type and a full subcategory of the homotopy category of E-infinity(F) over bar (p)-algebras . (C) 2000 Published by Elsevier Science Ltd. All rights reserved.