Nilpotence theorem

(Redirected from Nilpotence conjecture)

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.[1] It was conjectured by Douglas Ravenel (1984) and proved by Ethan S. Devinatz, Michael J. Hopkins, and Jeffrey H. Smith (1988).

Nishida's theorem

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Goro Nishida (1973) 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

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References

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  1. ^ Lurie, Jacob (April 27, 2010). "The Nilpotence Theorem (Lecture 25)" (PDF). Archived (PDF) from the original on January 30, 2022.

Further reading

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