symmetric monoidal (∞,1)-category of spectra
For each prime and for each natural number there is a Bousfield localization of spectra
where is the th Morava K-theory (for the given prime ). These arrange into the chromatic tower which for each spectrum is of the form
The chromatic convergence theorem states mild conditions under which the homotopy limit over this tower is the -localization
of .
In particular if is a finite p-local spectrum then the chromatic convergence theorem says that the homotopy limit over the chromatic tower of reproduces .
Since moreover is the homotopy fiber product
(see at smash product theorem and see this remark at fracture square ) it follows that in principle one may study any spectrum by understanding all its “chromatic pieces” . This is the topic of chromatic homotopy theory.
Last revised on December 14, 2015 at 14:23:19. See the history of this page for a list of all contributions to it.