Lubin-Tate Deformation Spaces and Fields of Norms

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 formal group X of finite height h, together with a Drinfeld level-n structure lambda. We choose principal prime ideals p(n) vertical bar (p) in each ring R-n in a compatible way and consider the field K-n' obtained by localizing R-n at p(n) and passing to the field of fractions of the completion. By taking the compositum K-n = K-n' K-0 of K-n(') with the completion K-0 of a certain unramified extension of K-0('), we obtain a tower of fields (K-n)(n) which we prove to be strictly deeply ramified in the sense of Scholl. When h = 2 we also investigate the question of whether this is a Kummer tower.