Morava K-theory

In stable homotopy theory, a branch of mathematics, Morava K-theory is one of a collection of cohomology theories introduced in algebraic topology by Jack Morava in unpublished preprints in the early 1970s. For every prime number "p" (which is suppressed in the notation), it consists of theories "K"("n") for each nonnegative integer "n", each a ring spectrum in the sense of homotopy theory. published the first account of the theories.
Details.
The theory "K"(0) agrees with singular homology with rational coefficients, whereas "K"(1) is a summand of mod-"p" complex K-theory. The theory "K"("n") has coefficient ring
where "v""n" has degree 2("p""n" − 1). In particular, Morava K-theory is periodic with this period, in much the same way that complex K-theory has period 2.
These theories have several remarkable properties.