Attached primes of the top local cohomology modules with respect to an ideal (II)

Details Attached primes of the top local cohomology modules with respect to an ideal (II) Attached primes of the top local cohomology modules with respect to an ideal (II)

2005-01-05

arxiv.org/abs/math/0501063v1

Mathematics

Commutative Algebra

9 pages

Scientific paper

For a finitely generated module $M$, over a commutative Noetherian local ring $(R, \mathfrak{m})$, it is shown that there exist only a finite number of non--isomorphic top local cohomology modules $\mathrm{H}_{\mathfrak{a}}^{\mathrm{dim} (M)}(M)$, for all ideals $\mathfrak{a}$ of $R$. We present a reduced secondary representation for the top local cohomology modules with respect to an ideal. It is also shown that for a given integer $r\geq 0$, if $\mathrm{H}_{\mathfrak{a}}^{r}(R/\mathfrak {p})$ is zero for all $\mathfrak{p}$ in $\mathrm{Supp}(M)$, then $\mathrm{H}_{\mathfrak{a}}^{i}(M)= 0$ for all $i\geq r$.

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