Boundedness of complements for fibered Fano threefolds in positive characteristic

Abstract

In this paper, we prove the canonical bundle formula for Fano type fibrations and Shokurov's conjecture on boundedness of complements for Fano type threefold pairs $(X,B)$ with fibration structures in large characteristics. In particular, we prove the conjecture when $-(K_X+B)\not\equiv 0$ is nef and not big in large characteristics.

41 pages, corrected some mistakes and typos