p-adic origamis

An origami is a finite covering of a torus which is ramified over only one point. Origamis can be defined algebraically over an arbitrary field. In these notes, after a short reminder of complex origamis, we focus on origamis over p-adic fields with special emphasis on those that can be represented by Mumford curves. These p-adic origamis, at least those which are normal coverings of the torus, have been classified by K. Kremer. The main goal of this paper is to give a little background on p-adic uniformization and thus to introduce the reader to Kremer's work, the main results of which are summarized in the last section.