Hrushovski proved some function field versions of the Mordell-Lang conjecture and gave an effective proof of the Manin-Mumford conjecture by using the trichotomy theorem for differential and difference fields to show that certain arithmetically defined groups have locally modular induced structure. One quotable version of the theorem takes the following form.
Theorem: Let K be a finitely generated field of positive characteristic and C a curve of genus at least two which is not isomorphic (even over the algebraic closure of K) to a curve over a finite field. Then there are only finitely many K-rational points on C.A full discussion of this work would take us too far afield. See the Lecture Notes in Logic volume on Hrushovski's Proof of the Mordell-Lang Conjecture for more details.