Graded-Injective Modules and Bass Numbers of Veronese Submodules
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929436562030592 |
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| author | Murray, Taylor |
| author_facet | Murray, Taylor |
| contents | Let $R$ be a standard graded, finitely generated algebra over a field, and let $M$ be a graded module over $R$ with all Bass numbers finite. Set $(-)^{(n)}$ to be the $n$-th Veronese functor. We compute the Bass numbers of $M^{(n)}$ over the ring $R^{(n)}$ for all prime ideals of $R^{(n)}$ that are not the homogeneous maximal ideal in terms of the Bass numbers of $M$ over $R$. As an application to local cohomology modules, we determine the Bass numbers of $H_{I\cap R^{(n)}}^i(R^{(n)})$ over the ring $R^{(n)}$ in the case where $H_I^i(R)$ has finite Bass numbers over $R$ and $I$ is a graded ideal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_17656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded-Injective Modules and Bass Numbers of Veronese Submodules Murray, Taylor Commutative Algebra 13A02, 13C11 (Primary) 13D45 (Secondary) Let $R$ be a standard graded, finitely generated algebra over a field, and let $M$ be a graded module over $R$ with all Bass numbers finite. Set $(-)^{(n)}$ to be the $n$-th Veronese functor. We compute the Bass numbers of $M^{(n)}$ over the ring $R^{(n)}$ for all prime ideals of $R^{(n)}$ that are not the homogeneous maximal ideal in terms of the Bass numbers of $M$ over $R$. As an application to local cohomology modules, we determine the Bass numbers of $H_{I\cap R^{(n)}}^i(R^{(n)})$ over the ring $R^{(n)}$ in the case where $H_I^i(R)$ has finite Bass numbers over $R$ and $I$ is a graded ideal. |
| title | Graded-Injective Modules and Bass Numbers of Veronese Submodules |
| topic | Commutative Algebra 13A02, 13C11 (Primary) 13D45 (Secondary) |
| url | https://arxiv.org/abs/2407.17656 |