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# Chromatic homotopy theory

In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, which is based on Quillen's work relating cohomology theories to formal groups. In this picture, theories are classified in terms of their "chromatic levels"; i.e., the heights of the formal groups that define the theories via the Landweber exact functor theorem. Typical theories it studies include: complex K-theory, elliptic cohomology, Morava K-theory and tmf.

See also

Redshift conjecture

Ravenel conjectures

Moduli stack of formal group laws

References

J. Lurie, Chromatic Homotopy Theory (252x)

External links

http://ncatlab.org/nlab/show/chromatic+homotopy+theory

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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