  I give a necessary and sufficient condition for a nef and big line bundle in
positive characteristic to be semi-ample, and then give two applications: I
show that the relative dualizing sheaf of the universal curve is semi-ample, in
positive characteristic, and give a simple example which shows that this, and
the semi-ampleness criterion, fail in characteristic zero. My second
application is to Mori's program for minimal models of 3-folds. I prove a
version of the Basepoint Free Theorem (for big line bundles on 3-folds of
positive characteristic) and a simple Cone Theorem, for 3-folds of positive
Kodaira dimension.
