Chromatic homotopy theory

Summary

Chromatic homotopy theory studies the stable homotopy category, one prime $p$ at a time, by splitting it into layers indexed by a height $n = 0, 1, 2, \ldots$. The height comes from the height of formal groups, through Quillen's theorem and Brown–Peterson cohomology. Each layer is seen by a Morava K-theory $K(n)$ and is governed by $v_n$-periodic phenomena. The nilpotence theorem and the other Ravenel conjectures proved by Devinatz, Hopkins, Ravenel and Smith are its foundations.