In mathematics, Morava K-theory is a collection of cohomology theories introduced in algebraic topology by Jack Morava . It consists of a doubly-indexed family of theories, each a ring spectrum in the sense of homotopy theory, called

K(n, p),

where n is a positive integer and p is a prime number. The motivation is to have theories that collectively rival complex cobordism, represented by the spectrum MU, while individually being easier to manipulate.

Each K(n, p) has a high degree of symmetry. The theory has mostly been developed in unpublished preprints of Morava.