Simplicial chains over a field and \(p\)-local homotopy theory. (English) Zbl 0849.55011
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 \(X\) [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.
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 \(X\) [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.
Reviewer: M.Golasiński (Toruń)
MSC:
| 55P60 | Localization and completion in homotopy theory |
| 55U35 | Abstract and axiomatic homotopy theory in algebraic topology |
| 18G30 | Simplicial sets; simplicial objects in a category (MSC2010) |
Keywords:
algebraic model; homotopy theory; simplicial set; coalgebra structure; chains; Bousfield localizationCitations:
Zbl 0309.55013References:
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