On endomorphism rings and dimensions of local cohomology modules
| dc.creator | Schenzel, Peter | |
| dc.date | 2008-06-27 | |
| dc.date.accessioned | 2026-07-07T09:47:08Z | |
| dc.date.available | 2026-07-07T09:47:08Z | |
| dc.description | Let $(R,\mathfrak m)$ denote an $n$-dimensional complete local Gorenstein ring. For an ideal $I$ of $R$ let $H^i_I(R), i \in \mathbb Z,$ denote the local cohomology modules of $R$ with respect to $I.$ If $H^i_I(R) = 0$ for all $i \not= c = \height I,$ then the endomorphism ring of $H^c_I(R)$ is isomorphic to $R$ (cf. \cite{HSt} and \cite{HS}). Here we prove that this is true if and only if $H^i_I(R) = 0, i = n, n -1$ provided $c \geq 2$ and $R/I$ has an isolated singularity resp. if $I$ is set-theoretically a complete intersection in codimension at most one. Moreover, there is a vanishing result of $H^i_I(R)$ for all $i > m, m$ a given integer, resp. an estimate of the dimension of $H^i_I(R).$ | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/0806.4433 | |
| dc.identifier | http://arxiv.org/abs/0806.4433 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163767 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D45; 13H10; 14M10 | |
| dc.title | On endomorphism rings and dimensions of local cohomology modules | |
| dc.type | text |