INTERSECTION DE RHAM COMPLEXES IN POSITIVE CHARACTERISTIC

We establish a positive characteristic analogue of intersection cohomology theory for variations of Hodge structure. It includes: a) the de Rham-Higgs comparison theorem for the intersection de Rham complex; b) the E1-degeneration theorem for the intersection de Rham complex of a periodic de Rham bundle; c) the Kodaira-Saito vanishing theorem for the intersection cohomology groups of a periodic Higgs bundle. These results generalize the Kodaira-Saito vanishing theorem of Arapura [Ar]. As an application, we give an algebraic proof of the E1-degeneration theo[KK], and the vanishing theorem of Saito [Sa] for VHSs of geometric origin.