Geodesic
Bousfield localization of ghost maps
Homology, homotopy, and applications, Tome 19 (2017) no. 1, pp. 371-389.

Voir la notice de l'article provenant de la source International Press of Boston

In homotopy theory, a ghost map is a map that induces the zero map on all stable homotopy groups. Bousfield localization is the homotopy-theoretic analogue of localization for rings and modules. In this paper, we consider the Bousfield localization of ghost maps. In particular, we pose the question: for which localization functors is it the case that the localization of a ghost is always a ghost? On the category of $p$-local spectra, we conjecture that the only localizations satisfying this property are the zero functor, the identity functor, and localization with respect to the rational Eilenberg–Mac Lane spectrum $H\mathbb{Q}$.We significantly narrow the field of possible counter-examples (one interesting outstanding possibility is the Brown–Comenetz dual of the sphere) and we consider a weaker version of the question at hand.
DOI : 10.4310/HHA.2017.v19.n1.a18
Classification : 55P42, 55P60
Keywords: Bousfield localization, ghost map, ghost-preserving localization 
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     title = {Bousfield localization of ghost maps},
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     pages = {371--389},
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Mark Hovey; Keir Lockridge. Bousfield localization of ghost maps. Homology, homotopy, and applications, Tome 19 (2017) no. 1, pp. 371-389. doi : 10.4310/HHA.2017.v19.n1.a18. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n1.a18/

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