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Morava K-theory is one of a collection of cohomology theories introduced in algebraic topology by Jack Morava in unpublished preprints in the early 1970s.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, it consists of theories K 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 agrees with singular homology with rational coefficients, whereas K is a summand of mod-p complex K-theory. The theory K has coefficient ring
where vn has degree 2. 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.