\(E_{\infty}\) algebras and \(p\)-adic homotopy theory
In the 1970's Sullivan established a contravariant equivalence between the homotopy categories of rational spaces and of commutative differential graded \(\mathbb Q\)-algebras. The present paper provides an analogous result for \(p\)-adic homotopy theory: The singular cochain functor with coefficients \(\overline{\mathbb F}_p\) (algebraic closure of \(\mathbb F_p\)) induces a contravariant equivalence from the homotopy category of \(p\)-complete nilpotent spaces of finite type to a full subcategory of the homotopy category of \(E_{\infty}\overline{\mathbb F}_p\)-algebras. The author also discusses the relationship between his approach and the work of others on \(p\)-adic homotopy theory.
scientific article; zbMATH DE number 1546932