Bass Numbers of Semigroup-Graded Local Cohomology
| dc.creator | Helm, David | |
| dc.creator | Miller, Ezra | |
| dc.date | 2000-10-01 | |
| dc.date | 2000-10-17 | |
| dc.date.accessioned | 2026-07-07T04:37:45Z | |
| dc.date.available | 2026-07-07T04:37:45Z | |
| dc.description | Given a module M over a ring R which has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology of M at any Q-graded ideal I in terms of Ext modules. This method is used to obtain finiteness results for the local cohomology of graded modules over semigroup rings; in particular we prove that for a semigroup Q whose saturation is simplicial, the Bass numbers of such local cohomology modules are finite. Conversely, if the saturation of Q is not simplicial, one can find a graded ideal I and a graded R-module M whose local cohomology at I in some degree has an infinite-dimensional socle. We introduce and exploit the combinatorially defined essential set of a semigroup. | |
| dc.description | 19 pages LaTeX, 1 figure (.eps) Definition 5.1 corrected; transcription error in Theorem 7.1.3 fixed | |
| dc.identifier | https://arxiv.org/abs/math/0010003 | |
| dc.identifier | http://arxiv.org/abs/math/0010003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60020 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 13D45 (Primary), 05E99 | |
| dc.title | Bass Numbers of Semigroup-Graded Local Cohomology | |
| dc.type | text |