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

Abstract

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