Abstract
One of the goals of this article is to describe the isomorphism between Lubin-Tate and Drinfeld towers at the level of their skeletons after taking quotient by GLn(OF)×OD× or I×OD×, where OD is the maximal order in the division algebra with invariant 1/n over F and I an Iwahori subgroup of GLn. We give applications to the theory of canonical subgroups on Lubin-Tate spaces, the description of spherical Hecke orbits in those spaces, fundamental domains for Hecke correspondences, and the Gross-Hopkins period mapping. We also study in detail the ramification filtrations (upper and lower) and the Hodge-Tate map of a one-dimensional formal p-divisible group
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