Vanishing via lifting to second Witt vectors and a proof of an isotriviality result

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A 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 pages

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