2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98189We use Cox's description for sheaves on toric varieties and results about the local cohomology with respect to monomial ideals to give a characteristic free approach to vanishing results on arbitrary toric varieties. As an application, we give a proof of a strong form of Fujita's conjecture in the case of toric varieties. We also prove that every sheaf on a toric variety corresponds to a module over the homogeneous coordinate ring, generalizing Cox's result for the simplicial case.21 pages. Revised version, to appear in Tohoku Mathematical JournalAlgebraic GeometryCommutative Algebra14M25 (Primary); 14F17 (Secondary)text