Open loci of graded modules
| dc.creator | Rotthaus, Christel | |
| dc.creator | Sega, Liana M. | |
| dc.date | 2004-03-23 | |
| dc.date.accessioned | 2026-07-07T05:06:41Z | |
| dc.date.available | 2026-07-07T05:06:41Z | |
| dc.description | Let $A=\oplus_{i\in \nn}A_i$ be an excellent homogeneous Noetherian graded ring and let $M=\oplus_{n\in \zz}M_n$ be a finitely generated graded $A$-module. We consider $M$ as a module over $A_0$ and show that the $(S_k)$-loci of $M$ are open in $\Spec(A_0)$. In particular, the Cohen-Macaulay locus $U^0_{CM}=\{\p\in \Spec(A_0) \mid M_\p {is Cohen-Macaulay}\}$ is an open subset of $\Spec(A_0)$. We also show that the $(S_k)$-loci on the homogeneous parts $M_n$ 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 $I\subseteq A$ which is not contained in any minimal prime of $M$ the $(S_k)$-loci for the modules $M/I^nM$ are eventually stable. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403399 | |
| dc.identifier | http://arxiv.org/abs/math/0403399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70566 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 13A02, 13H10 | |
| dc.title | Open loci of graded modules | |
| dc.type | text |