Simplicial chains over a field and \(p\)-local homotopy theory
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.
scientific article; zbMATH DE number 856579