Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 ; Department of Mathematics and Statistics, University of Missouri, Kansas City, Missouri 64110-2499
Abstract:
Let be an excellent homogeneous Noetherian graded ring and let be a finitely generated graded -module. We consider as a module over and show that the -loci of are open in . In particular, the Cohen-Macaulay locus is Cohen-Macaulay is an open subset of . We also show that the -loci on the homogeneous parts of are eventually stable. As an application we obtain that for a finitely generated Cohen-Macaulay module over an excellent ring and for an ideal which is not contained in any minimal prime of , the -loci for the modules are eventually stable.