Morava K-theory 
at a prime 
and positive integer height
is the generalized homology theory with
coefficient ring
![K(n)_*=F_p[v_n,v_n^(-1)],](/images/equations/MoravaK-Theory/NumberedEquation1.svg) |
where 
.
The height-zero convention is rational homology, 
. For a nonzero finite 
-local spectrum, its
chromatic type is the least 
for which its 
homology is nonzero.
Localization 
retains the height-
information and is different from localization at the sum
of all heights through 
.
It is used in sphere finiteness and chromatic
fixed-point loss.
