2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122299Let S be a standard N^k-graded polynomial ring over a field. Let I be a multigraded homogeneous ideal in S and let M be a finitely generated Z^k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I^nM is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.Final version to appear in J. Algebra; 18 pagesCommutative AlgebraAlgebraic Geometry13D02; 13D45; 14B15; 14F17text