Relative semi-ampleness in positive characteristic

Abstract

Given an invertible sheaf on a fibre space between projective varieties of positive characteristic, we show that fibrewise semi-ampleness implies relative semi-ampleness. The same statement fails in characteristic zero.

56 pages. This version corrects a gap in the proof of Theorem 2.30 in the published version, kindly pointed out to us by Adrian Langer. The issue affects Proposition 3.2, where Theorem 2.30 was used. The only change is the addition of Section 8, which gives a new proof of Proposition 3.2 avoiding Theorem 2.30. The main results are unchanged