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 ${\displaystyle \mathrm {MU} }$. More precisely, it states that for any ring spectrum ${\textstyle R}$, the kernel of the map ${\textstyle \pi _{\ast }R\to \mathrm {MU} _{\ast }(R)}$ 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).