Frobenius splitting for some Abelian fiber spaces

In this paper, we study the Frobenius split property of fibrations over curves via the relative Frobenius morphism. In particular, we can classify Frobenius split Abelian fiber spaces over curves which has no wild fibers in terms of the degree of the top higher direct image Rn−1π⁎OX, the multiplicities of multiple fibers, non-ordinary points, and the characteristic of the base field.