The isomorphism between the Drinfeld and Lubin-Tate spaces at infinite level

Introduction

In their book on period spaces for p-divisible groups, Rapoport and Zink conjecture a certain duality on the data giving rise to moduli spaces of p-divisible groups, producing an equivariant isomorphism of the generic fibers of the corresponding moduli spaces at infinite level. As a special case of their conjecture, one can recover the famous isomorphism between the Lubin-Tate and Drinfeld spaces at infinite level. This workshop will give a modern proof of this isomorphism using the theory of local shtukas as developed by Scholze and Weinstein in the Berkeley notes, and explore its application to the Jacquet-Langlands correspondence following the work of Hansen and Mann.