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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29714 |
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| _version_ | 1866911654120259584 |
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| author | Shibata, Kosuke Yanagawa, Kohji |
| author_facet | Shibata, Kosuke Yanagawa, Kohji |
| contents | For a simplicial poset $P$, Stanley assigned the face ring $A_P$, which is the quotient of the polynomial ring $S:=K[t_x \mid x \in P \setminus \{\widehat{0} \}]$ by the ideal $I_P$. This is a generalization of Stanley-Reisner rings, but $S$ and $A_P$ are not standard graded in this case, and $I_P$ is not a monomial ideal. To establish the foundation of the theory on local cohomology $H_{I_p}^i(S)$ and its injective resolution, we give an explicit description of the graded injective envelope ${}^*\! E_S(S/\mathfrak{p}_x)$, where $\mathfrak{p}_x$is the prime ideal associated with $x \in P$, and analyze their behavior in the graded dualizing complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29714 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toward the theory on local cohomologies at the ideals given by simplicial posets Shibata, Kosuke Yanagawa, Kohji Commutative Algebra 13F55, 13C11, 13D45 For a simplicial poset $P$, Stanley assigned the face ring $A_P$, which is the quotient of the polynomial ring $S:=K[t_x \mid x \in P \setminus \{\widehat{0} \}]$ by the ideal $I_P$. This is a generalization of Stanley-Reisner rings, but $S$ and $A_P$ are not standard graded in this case, and $I_P$ is not a monomial ideal. To establish the foundation of the theory on local cohomology $H_{I_p}^i(S)$ and its injective resolution, we give an explicit description of the graded injective envelope ${}^*\! E_S(S/\mathfrak{p}_x)$, where $\mathfrak{p}_x$is the prime ideal associated with $x \in P$, and analyze their behavior in the graded dualizing complex. |
| title | Toward the theory on local cohomologies at the ideals given by simplicial posets |
| topic | Commutative Algebra 13F55, 13C11, 13D45 |
| url | https://arxiv.org/abs/2603.29714 |