# Contents

## Definition

For some prime number $p$, let $X$ be a finite p-local spectrum. By the periodicity theorem this carries a $v_k$-self map

$f \;\colon\; \Sigma^k X \longrightarrow X \,.$

The telescopic localization of $X$ is the homotopy colimit $X[f^{-1}]$ of the direct sequence

$X \stackrel{\Omega^k f}{\longrightarrow} \Sigma^{-k} X \stackrel{\Omega^{2k} f}{\longrightarrow} \Sigma^{-2k} X \stackrel{}{\longrightarrow} \cdots \,.$

For $X$ in addition of type $\gt n$, this is a Bousfield localization of spectra. (Lurie 10, prop. 1)

## References

Lecture notes include

Created on November 12, 2013 at 09:23:26. See the history of this page for a list of all contributions to it.