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We construct a tower of fields from the rings $R_n$ which parametrize pairs$(X,\lambda)$, where $X$ is a deformation of a fixed one-dimensional formalgroup $\mathbb{X}$ of finite height $h$, together with a Drinfeld level-$n$structure $\lambda$. We choose principal prime ideals $\mathfrak{p}_n \mid (p)$in each ring $R_n$ in a compatible way and consider the field $K'_n$ obtainedby localizing $R_n$ at $\mathfrak{p}_n$, completing, and passing to thefraction field. By taking the compositum $K_n = K'_n K_0$ of each field withthe completion $K_0$ of a certain unramified extension of $K'_0$, we obtain atower of fields $(K_n)_n$ which we prove to be strictly deeply ramified in thesense of Anthony Scholl. When $h=2$ we also investigate the question of whetherthis is a Kummer tower.

Lubin-Tate Deformation Spaces and Fields of Norms