  Let p: Y--> X be a surjection between schemes projective over the algebraic
closure of a finite field. Let L be a line bundle on X such that p^*(L) is
globally generated. I give a natural necessary and sufficient condition under
which some positive tensor power of L is globally generated. I apply this to
give a sufficient condition for semi-ampleness of nef line bundles on the
moduli space of stable pointed curves, in positive characteristic.

Algebraic Geometry