# Abstract Thomas Zink

**Thomas Zink**will speak on

** Interpretations of the p-adic space Ωd as a moduli space**

**Abstract:** This space was introduced by Deligne. It is formally similar to the Siegel upper half plane. Drinfeld showed that Ωd is a moduli space of certain formal p-divisible groups. As a consequence reproved Cherednik’s uniformization theorem for Shimura curves and he discovered that Ωd has non trivial ́etale coverings. Kudla and Rapoport discovered an alternative description of Ω2 as a moduli space.

In this lecture we discuss further moduli problems which lead to Ωd . We show how to pass from one problem to another by using the theory of displays of formal p-divisible groups. This is joint work with S. Kudla and M. Rapoport.