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