2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77763A proof based on reduction to finite fields of Esnault-Viehweg's stronger version of Sommese Vanishing Theorem for $k$-ample line bundles is given. This result is used to give different proofs of isotriviality results of A. Parshin and L. Migliorini.Latex, 7 pagesAlgebraic GeometryVanishing via lifting to second Witt vectors and a proof of an isotriviality resulttext