2004/03/23 by Christel Rotthaus, Rotthaus, Christel, Liana M. Şega +2
Computer Science · Mathematics · #13A02 #13H10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AC #math.RA #msc:13A02 #msc:13H10
paper · pdf · doi:10.48550/arxiv.math/0403399
22 pages
arxiv created 2004/03/23 · openalex publication_date 2004/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A=⊕i∈ \nnAi be an excellent homogeneous Noetherian graded ring and let M=⊕n∈ \zzMn be a finitely generated graded A-module. We consider M as a module over A0 and show that the (Sk)-loci of M are open in \Spec(A0). In particular, the Cohen-Macaulay locus U0CM=\\p∈ \Spec(A0) | M_\p is Cohen-Macaulay\ is an open subset of \Spec(A0). We also show that the (Sk)-loci on the homogeneous parts Mn of M are eventually stable. As an application we obtain that for a finitely generated Cohen-Macaulay module M over an excellent ring A and for an ideal I⊆ A which is not contained in any minimal prime of M the (Sk)-loci for the modules M/InM are eventually stable.