David Harbater, University of Pennsylvania

Lifting branched covers of algebraic curves

Branched covers of algebraic curves are well understood over the complex numbers, from the point of view of Riemann surfaces. But they are more mysterious over other fields, especially in characteristic p. One approach to studying such covers is to "lift" them to characteristic 0; this raises the question of which covers can be lifted, and which covering groups guarantee the existence of a lift. This talk, which describes joint work with T. Chinburg and R. Guralnick, considers these questions, which relate to a conjecture of F. Oort.