nLab 2-periodic Morava K-theory

Idea

The 2-periodic ring spectrum-version of Morava K-theory.

Let $C$ be any elliptic curve over the prime field $\mathbb{F}_p$. This will have a formal group of either height $h=1$ (“ordinary curve”) or height $h=2$ (“supersingular elliptic curve”). For any such $C$, there is a ring spectrum $K_C$ with coefficient ring $\pi_* K_C=\mathbb{F}_p[u,u^{-1}]$, with $u\in \pi_2$, which is complex orientable, whose formal group is the formal group of $C$. This $K_C$ is the “2-periodic Morava $K$-theory” associated to the formal group.

(grapped from this MO comment by Charles Rezk).