Homological localizations of Eilenberg-Mac Lane spectra

Javier J. Guti\'errez
javier.gutierrez@ub.edu

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 $p$.