nLab
telescope conjecture

Idea

In the stable homotopy category of $p$-local spectra for some prime number $p$, there are two collections of similarly behaved spectra: the Morava K-theories and spectra which are the telescopes of finite spectra? under their $v_n$-maps. The former are usually denoted $K(n)$ and the latter are often denoted $T(n)$. The telescope conjecture is that localization at $K(n)$ and localization at $T(n)$ are (Bousfield) equivalent?.