Nilpotence theorem

Template:Short description In algebraic topology, the nilpotence theorem gives a condition for an element in the homotopy groups of a ring spectrum to be nilpotent, in terms of the complex cobordism spectrum $\mathrm{M}\mathrm{U}$. More precisely, it states that for any ring spectrum $R$, the kernel of the map ${\pi }_{\ast }R\to {\mathrm{M}\mathrm{U}}_{\ast }(R)$ consists of nilpotent elements. It was conjectured by Template:Harvs and proved by Template:Harvs.

Nishida's theorem

Template:Harvs showed that elements of positive degree of the homotopy groups of spheres are nilpotent. This is a special case of the nilpotence theorem.

See also

• Ravenel's conjectures

References

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Further reading

• Connection of X(n) spectra to formal group laws