Arithmetic and Geometry of the Open p-adic Disc
Scott Corry

In this talk I will discuss a recent result concerning Galois covers of the open p-adic disc. Roughly speaking, it says that the special fibre of such a cover is determined by the specializations of the cover at points of the disc with residue characteristic zero. This result has applications to lifting problems, and in particular allows for a characteristic zero reformulation of the Oort Conjecture concerning the liftability of cyclic covers of curves.