The support of top graded local cohomology modules
| dc.creator | Katzman, Mordechai | |
| dc.date | 2003-12-17 | |
| dc.date.accessioned | 2026-07-07T05:03:59Z | |
| dc.date.available | 2026-07-07T05:03:59Z | |
| dc.description | Let $R_0$ be any domain, let $R=R_0[U_1, ..., U_s]/I$, where $U_1, ..., U_s$ are indeterminates of some positive degrees, and $I\subset R_0[U_1, ..., U_s]$ is a homogeneous ideal. The main theorem in this paper is states that all the associated primes of $H:=H^s_{R_+}(R)$ contain a certain non-zero ideal $c(I)$ of $R_0$ called the ``content'' of $I$. It follows that the support of $H$ is simply $V(\content(I)R + R_+)$ (Corollary 1.8) and, in particular, $H$ vanishes if and only if $c(I)$ is the unit ideal. These results raise the question of whether local cohomology modules have finitely many minimal associated primes-- this paper provides further evidence in favour of such a result. Finally, we give a very short proof of a weak version of the monomial conjecture based on these results. | |
| dc.identifier | https://arxiv.org/abs/math/0312333 | |
| dc.identifier | http://arxiv.org/abs/math/0312333 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69632 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | The support of top graded local cohomology modules | |
| dc.type | text |