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Ando established an algebraic criterion for when a complex orientation for aMorava E-theory is an $H_\infty$-map. The criterion relates such an orientationto a specific property of the formal group associated to the E-theory, namely,a norm coherence condition on its coordinate. On the other hand, Colemanconstructed a norm operator for interpolating division values in local fields,which depends on a Lubin--Tate formal group law. These formal group laws areimportant tools in explicit local class field theory. In this article, we givea conceptual proof for Ando's theorem using the Coleman norm operator via thebridge of formal group laws between topology and arithmetic.

A proof for Ando's theorem on norm-coherent coordinates via the Coleman norm operator