E∞ algebras and p-adic homotopy theory

Abstract

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.