Morava K-theory

Summary

Morava K-theory is a family of generalized cohomology theories $K(n)$, one for each prime $p$ and each integer $n \ge 1$. Its coefficient ring $\F_p[v_n, v_n^{-1}]$ is a graded field, so it behaves almost like ordinary cohomology with coefficients in a field. Its formal group law has height exactly $n$. These theories are the basic building blocks of chromatic homotopy theory, where they detect the layers of the stable homotopy category.