For each prime integer there exists a sequence of generalized homology theories (equivalently spectra) indexed by the non-negative integers, with the following properties:
- and when is all torsion.
- is one of isomorphic summands of mod- complex topological K-theory.
- and for , where . This ring is a graded field in the sense that every graded module over it is free. is a module over .
- There is a Künneth isomorphism:
- Let be a p-local finite CW-complex. If vanishes then so does .
- If as above is not contractible then .
Connection to Bousfield lattice
It is known that in the Bousfield lattice of the stable homotopy category, the Bousfield classes of the Morava K-theories are minimal. It is conjectured by Mark Hovey and John Palmieri that the Boolean algebra contained in the Bousfield lattice is atomic and generated by the Morava K-theories and the spectra which measure the failure of the telescope conjecture.
D. Ravenel, Nilpotence and Periodicity in Stable Homotopy Theory, Annals of Mathematics Studies 128, Princeton University Press (1992).
Morava E-theory and Morava K-theory Lecture notes (pdf)
Revised on April 10, 2013 15:20:24
by Urs Schreiber