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Morava E-Theory

Morava E-theory at height n and prime p is the even-periodic cohomology theory associated with the universal deformation of a height-n formal group over a perfect field of characteristic p. For the Honda formal group over F_(p^n) its degree-zero coefficient ring is

E_0=W(F_(p^n))[[u_1,...,u_(n-1)]].

The full coefficient ring is E_*=E_0[u,u^(-1)], with u in degree -2. The nonextended Morava stabilizer group is the automorphism group of the Honda formal group and acts on the deformation ring. The invariant prime ideals and their relationship to thick tensor ideals appear in the Hovey-Strickland conjecture.

See also

Formal Group, Hovey-Strickland Conjecture, Morava K-Theory, Witt Vector

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References

Hovey, M. and Strickland, N. P. Morava K-Theories and Localisation. Providence, RI: Amer. Math. Soc., 1999. https://doi.org/10.1090/memo/0666.Rezk, C. Lectures on Power Operations. Version 0.11, July 15, 2024. https://www.rezk.web.illinois.edu/power-operation-lectures.pdf.

Cite this as:

Weisstein, Eric W. "Morava E-Theory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MoravaE-Theory.html

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