nLab
2-periodic Morava K-theory

Idea

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

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

(grapped from this MO comment by Charles Rezk).

Last revised on March 16, 2017 at 10:59:45. See the history of this page for a list of all contributions to it.