Nilpotence theorem

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 . More precisely, it states that for any ring spectrum , the kernel of the map consists of nilpotent elements. It was conjectured by and proved by .

Nishida's theorem

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

. Open online version.

Further reading Connection of X(n) spectra to formal group laws