Spherical Completeness, Coherence, and GCD Properties of Formal Power Series and Witt Vector Rings

Yiding Wang

Let $K$ be a complete nonarchimedean valued field with $v(K^{\times })=\mathbf{R}$, and let $V={\mathcal{O}}_K$. We prove that $K$ is spherically complete if and only if $V[[T]]$ is coher…