Bousfield localization of a spectrum 
with respect to a spectrum 
is a map 
inducing an isomorphism
on 
homology and having an 
-local target. A target is 
-local when maps to it from every 
-acyclic spectrum vanish
in every shift. An 
-acyclic spectrum 
satisfies 
. The localization map is universal for maps from 
to local spectra.
In chromatic homotopy theory, 
denotes localization at Morava
K-theory and 
denotes localization at the Johnson-Wilson spectrum 
.
The latter has the same acyclics as the sum of 
through 
. Thus 
is rationalization. The overlap 
is the object in chromatic splitting
questions.
