Seshadri constants in positive characteristic

Abstract Seshadri constants measure the local positivity of an ample line bundle at a point. In characteristic 0, vanishing theorems imply that lower bounds on the Seshadri constants of a line bundle have nice consequences for the corresponding adjoint line bundle. I will explain how similar results can be proved in positive characteristic by making use of the Frobenius morphism. This is based on joint work with Karl Schwede.