  We prove finiteness results on integral points on complements of large
divisors in projective varieties over finitely generated fields of
characteristic zero. To do so, we prove a function field analogue of arithmetic
finiteness results of Corvaja-Zannier and Levin using Wang's function field
Subspace Theorem. We then use a method of Evertse-Gy\H{o}ry for concluding
finiteness of integral points over finitely generated fields from known
finiteness results over number fields.
