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Nilpotence theorem
On when an element of the coefficient ring of a ring spectrum is nilpotent From Wikipedia, the free encyclopedia
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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).
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Nishida's theorem
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.
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