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

Hongxiang Zhao

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arXiv · 2310.09837

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

Hongxiang Zhao

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Abstract

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.

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Hongxiang Zhao. 2023-10-15. A proof for Ando's theorem on norm-coherent coordinates via the Coleman norm operator. https://arxiv.org/abs/2310.09837

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