Operations and co-operations in Morava $E$-theory

Let $E=E_{n}$ denote the Morava $E$-theory spectrum, and let $\Gamma$ be the Morava stabilizer group of ring spectrum isomorphisms of $E$. We revisit the isomorphism $\pi_{*}L_{K(n)}(E\smash E)\cong C(\Gamma, E_{*})$ of graded formal Hopf algebroids, and its dual isomorphism $E^{*}E\cong E_{*}[[\Gamma]]$.

Keywords

Morava $E$-theory, Hopf algebroid, Morava stabilizer group, cohomology operations, twisted completed group ring

2010 Mathematics Subject Classification

55N22, 55P42, 57T05

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Published 1 January 2004