\(E_{\infty}\) algebras and \(p\)-adic homotopy theory
type: Item
instance of: scholarly article
title: \(E_{\infty}\) algebras and \(p\)-adic homotopy theory
zbMATH Open document ID: 0974.55004
DOI: 10.1016/S0040-9383(99)00053-1
author: Michael A. Mandell
published in: Topology
publication date: 2001-03-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 1546932
reviewed by: George Peschke
MaRDI profile type: Publication
full work available at URL: s0040-9383(99)00053-1
OpenAlex ID: W2053492560
description: scientific article; zbMATH DE number 1546932