Associate primes of local cohomology modules over certain quotients of regular rings
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916662973825024 |
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| author | Puthenpurakal, Tony J. |
| author_facet | Puthenpurakal, Tony J. |
| contents | Let $R$ be a regular ring containing a field $k$. Let $\mathbf{x} = x_1, \ldots, x_r$ be a regular sequence in $R$ such that $R/(\mathbf{x})$ is a regular ring. Fix $m \geq 1$. Set $A_m = R/(\mathbf{x})^m$. We show that for any ideal $Q$ of $A_m$ the set $\text{Ass} \ H^i_Q(A_m)$ is a finite set for $i \geq 0$, in the following cases:
1. $\text{char}\ k = p > 0$.
2. $\text{char} \ k = 0$, $R$ is local or a smooth affine algebra over $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Associate primes of local cohomology modules over certain quotients of regular rings Puthenpurakal, Tony J. Commutative Algebra Primary 13D45, 13A30, Secondary 13N10, 14B15 Let $R$ be a regular ring containing a field $k$. Let $\mathbf{x} = x_1, \ldots, x_r$ be a regular sequence in $R$ such that $R/(\mathbf{x})$ is a regular ring. Fix $m \geq 1$. Set $A_m = R/(\mathbf{x})^m$. We show that for any ideal $Q$ of $A_m$ the set $\text{Ass} \ H^i_Q(A_m)$ is a finite set for $i \geq 0$, in the following cases: 1. $\text{char}\ k = p > 0$. 2. $\text{char} \ k = 0$, $R$ is local or a smooth affine algebra over $k$. |
| title | Associate primes of local cohomology modules over certain quotients of regular rings |
| topic | Commutative Algebra Primary 13D45, 13A30, Secondary 13N10, 14B15 |
| url | https://arxiv.org/abs/2503.20539 |