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telescopic localization

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Definition

For some prime number pp, let XX be a finite p-local spectrum. By the periodicity theorem this carries a v kv_k-self map

f:Σ kXX. f \;\colon\; \Sigma^k X \longrightarrow X \,.

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

XΩ kfΣ kXΩ 2kfΣ 2kX. X \stackrel{\Omega^k f}{\longrightarrow} \Sigma^{-k} X \stackrel{\Omega^{2k} f}{\longrightarrow} \Sigma^{-2k} X \stackrel{}{\longrightarrow} \cdots \,.

For XX in addition of type >n\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.