2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98557We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing theorems, and used to study Milnor fibers of line arrangements, and hypersurface arrangements.LaTeX, 10 pagesAlgebraic GeometryCombinatorics32S22, 52C35, 55N25text