On the canonical bundle formula for abelian fiber spaces in positive characteristic

Abstract

Let X be a non-singular projective (n + 1)-fold defined over an algebraically closed field k of characteristic p ≥ 0, and B be a non-singular complete curve defined over k. A surjective morphism f : X → B is said to be an n-abelian fiber space if almost all fibers are n-dimensional abelian varieties. We examine the canonical bundle formula for n-abelian fiber spaces.