Graded-Injective Modules and Bass Numbers of Veronese Submodules
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.17656
- arXiv:
- arXiv:2407.17656
- Bibcode:
- 2024arXiv240717656M
- Keywords:
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- Mathematics - Commutative Algebra;
- 13A02;
- 13C11 (Primary) 13D45 (Secondary)
- E-Print:
- 29 pages. Comments welcome