Homological localizations of Eilenberg-Mac Lane spectra

Details Homological localizations of Eilenberg-Mac Lane spectra Homological localizations of Eilenberg-Mac Lane spectra

2005-11-16

arxiv.org/abs/math/0511412v1

Forum Mathematicum. Volume 22, Issue 2 (2010) p. 349-356

Mathematics

Algebraic Topology

9 pages

Scientific paper

We discuss the Bousfield localization $L_E X$ for any spectrum $E$ and any $HR$-module $X$, where $R$ is a ring with unit. Due to the splitting property of $HR$-modules, it is enough to study the localization of Eilenberg-Mac Lane spectra. Using general results about stable $f$-localizations, we give a method to compute the localization of an Eilenberg-Mac Lane spectrum $L_E HG$ for any spectrum $E$ and any abelian group $G$. We describe $L_E HG$ explicitly when $G$ is one of the following: finitely generated abelian groups, $p$-adic integers, Pr\"ufer groups, and subrings of the rationals. The results depend basically on the $E$-acyclicity patterns of the spectrum $H\Q$ and the spectrum $H\Z/p$ for each prime $p$.

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