This talk describes joint work with Ted Chinburg and Bob Guralnick, on the problem of lifting Galois covers of curves from characteristic p to characteristic 0 (i.e. to mixed characteristic). Frans Oort had conjectured that if G is a cyclic group, then every G-Galois branched cover in characteristic p lifts. This is known, for example, if G is cyclic of order p or p^2. More generally we call a finite group G an Oort group if it has this property. This talk will present results on the structure of Oort groups.