Bass numbers of graded components of local cohomology modules
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916004673617920 |
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| author | Jahangiri, Maryam |
| author_facet | Jahangiri, Maryam |
| contents | Let $R=\bigoplus_{n\in \NN_0}R_n$ be a standard graded ring, $R_+=\bigoplus_{n\in \NN}R_n$ its irrelevant ideal, and $M$ a finitely generated graded $R$-module. In this paper, we study the asymptotic behavior of the sequence $\{μ^i(\p_0, H^j_{R_+}(M)_n)\}_{n\in \Z}$ of Bass numbers of graded components of local cohomology modules with respect to an ideal $\p_0\in \Spec(R_0)$ in each of the following cases:
(1) $i=0$ or $i= 1$ and $j\leq f_{R_+}(M)$,
(2) $R_0$ is regular,
$i= \hei(\p_0)$ or $i= \hei(\p_0)- 1$ and $j= \cd_{R_+}(M)$,
(3) $M$ is relative Cohen-Macaulay with respect to $R_+$.
Here, $\cd_{R_+}(M)$ and $f_{R_+}(M)$ denote the cohomological dimension and finiteness dimension of $M$ with respect to $R_+$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11943 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bass numbers of graded components of local cohomology modules Jahangiri, Maryam Commutative Algebra 13A02, 13D45, 13D02, 13C11, 13E05 Let $R=\bigoplus_{n\in \NN_0}R_n$ be a standard graded ring, $R_+=\bigoplus_{n\in \NN}R_n$ its irrelevant ideal, and $M$ a finitely generated graded $R$-module. In this paper, we study the asymptotic behavior of the sequence $\{μ^i(\p_0, H^j_{R_+}(M)_n)\}_{n\in \Z}$ of Bass numbers of graded components of local cohomology modules with respect to an ideal $\p_0\in \Spec(R_0)$ in each of the following cases: (1) $i=0$ or $i= 1$ and $j\leq f_{R_+}(M)$, (2) $R_0$ is regular, $i= \hei(\p_0)$ or $i= \hei(\p_0)- 1$ and $j= \cd_{R_+}(M)$, (3) $M$ is relative Cohen-Macaulay with respect to $R_+$. Here, $\cd_{R_+}(M)$ and $f_{R_+}(M)$ denote the cohomological dimension and finiteness dimension of $M$ with respect to $R_+$, respectively. |
| title | Bass numbers of graded components of local cohomology modules |
| topic | Commutative Algebra 13A02, 13D45, 13D02, 13C11, 13E05 |
| url | https://arxiv.org/abs/2605.11943 |