On the formal cohomology of local rings
| dc.creator | Schenzel, Peter | |
| dc.date | 2007-04-16 | |
| dc.date.accessioned | 2026-07-07T07:56:43Z | |
| dc.date.available | 2026-07-07T07:56:43Z | |
| dc.description | Let $\mathfrak a$ denote an ideal of a local ring $(R, \mathfrak m).$ Let $M$ be a finitely generated $R$-module. There is a systematic study of the formal cohomology modules $\varprojlim \HH^i(M/\mathfrak a^nM), i \in \mathbb Z.$ We analyze their $R$-module structure, the upper and lower vanishing and non-vanishing in terms of intrinsic data of $M,$ and its functorial behavior. These cohomology modules occur in relation to the formal completion of the punctured spectrum $\Spec R \setminus V(\mathfrak m).$ As a new cohomological data there is a description on the formal grade $\fgrade(\mathfrak a, M)$ defined as the minimal non-vanishing of the formal cohomology modules. There are various exact sequences concerning the formal cohomology modules. Among them a Mayer-Vietoris sequence for two ideals. It applies to new connectedness results. There are also relations to local cohomological dimensions. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0704.2005 | |
| dc.identifier | http://arxiv.org/abs/0704.2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127415 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D45; 14B15 | |
| dc.title | On the formal cohomology of local rings | |
| dc.type | text |