Simplicial chains over a field and \(p\)-local homotopy theory
type: Item
instance of: scholarly article
title: Simplicial chains over a field and \(p\)-local homotopy theory
zbMATH Open document ID: 0849.55011
DOI: 10.1007/BF02572629
published in: Mathematische Zeitschrift
publication date: 1996-11-05T00:00:00Z
full work available at URL: https://eudml.org/doc/174824
review text: The aim of the paper is to establish an algebraic model for homotopy theory at characteristics other than zero. If \(X\) is a simplicial set and \(F\) a field then the diagonal map \(X \to X \times X\) yields a simplicial cocommutative coalgebra structure on the chains \(FX\) of \(X\) with coefficients in \(F\). For an algebraically closed field \(F\) the author obtains the Bousfield localization of \(X\) [\textit{A. K. Bousfield}, Topology 14, 133-150 (1975; Zbl 0309.55013)] by means of \(FX\). Next, an appropriate generalization for a perfect and non-algebraically closed field \(F\) is presented.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18G30
zbMATH DE Number: 856579
zbMATH Keywords: algebraic model
zbMATH Keywords: homotopy theory
zbMATH Keywords: simplicial set
zbMATH Keywords: coalgebra structure
zbMATH Keywords: chains
zbMATH Keywords: Bousfield localization
author: Paul Goerss
MaRDI profile type: Publication
cites work: The localization of spaces with respect to homology
cites work: Lectures on \(p\)-divisible groups
cites work: Q4773818
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cites work: \(p\)-adic homotopy theory
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cites work: Homotopical algebra
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cites work: HOMOTOPY THEORY OF COALGEBRAS
OpenAlex ID: W2023148381
description: scientific article; zbMATH DE number 856579