In the stable homotopy category of -local spectra for some prime number , there are two collections of similarly behaved spectra: the Morava K-theories and spectra which are the telescopes of finite spectra under their -maps. The former are usually denoted and the latter are often denoted . The telescope conjecture is that localization at and localization at are (Bousfield) equivalent.
The conjecture is known to be true for . A disproof of this conjecture for using algebraic K-theory has been released by Burklund-Hahn-Levy-Schlank.
Last revised on October 27, 2023 at 04:31:41. See the history of this page for a list of all contributions to it.