Abstract
Let $K$ be a nonarchimedean local field, let $h$ be a positive integer, and denote by $D$ the central division algebra of invariant $1/h$ over $K$. The modular towers of Lubin-Tate and Drinfeld provide period rings leading to an equivalence between a category of certain $\mathrm{GL}_h(K)$-equivariant vector bundles on Drinfeld's upper half space of dimension $h-1$ and a category of certain $D^*$-equivariant vector bundles on the $(h-1)$-dimensional projective space.
