2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128882Let S be a standard N^r-graded algebra over a local ring A, and let M be a finitely generated Z^r-graded S-module. We characterize the Cohen-Macaulayness of M in terms of the vanishing of certain sheaf cohomology modules. As a consequence, we apply our result to study the Cohen-Macaulayness of multi-Rees modules (also called Rees modification). Our work extends previous studies on the Cohen-Macaulayness of multi-Rees algebras.16 pagesCommutative AlgebraAlgebraic Geometry13A30; 13C14; 14B15; 14M05text