Morava K-theory

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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. The theory has mostly been developed in unpublished preprints of Morava.

The theory K(n, p) has coefficient ring F_p[v_n,1/v_n] where v_n has degree −2(pⁿ−1), so in particular has this number as a period, in much the same way that complex K-theory has period 2.

[edit] References

• Johnson, David Copeland & Wilson, W. Stephen (1975), “BP operations and Morava's extraordinary K-theories.”, Math. Z. 144 (1): 55-75, MR0377856, DOI 10.1007/BF01214408 
• Würgler, Urs (1991), “Morava K-theories: a survey”, Algebraic topology Poznan 1989, vol. 1474, Lecture Notes in Math., Berlin: Springer, pp. 111-138, MR1133896, ISBN 978-3-540-54098-4, DOI 10.1007/BFb0084741