2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64467A conjecture of Kato says that the monodromy operator on the cohomology of a semi-stable degeneration of projective varieties is represented by an algebraic cycle on the special fiber of a normal crossing model of the fiber product degeneration. We prove this conjecture in the simple case of a semi-stable degeneration arising from a Lefschetz fibration.Algebraic GeometryNumber Theory14F42The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrationstext