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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2410.18493 |
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| _version_ | 1866913561751584768 |
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| author | Puthenpurakal, Tony J. |
| author_facet | Puthenpurakal, Tony J. |
| contents | Let $R$ be a regular ring of dimension $d$ containing a field $K$ of characteristic zero. If $E$ is an $R$-module let $Ass^i E = \{ Q \in \ Ass E \mid \ height Q = i \}$. Let $P$ be a prime ideal in $R$ of height $g$. We show that if $R/P$ satisfies Serre's condition $R_i$ then $Ass^{g+i+1}H^{g+1}_P(R)$ is a finite set. As an application of our techniques we prove that if $P$ is a prime ideal in $R$ such that $(R/P)_\mathfrak{q}$ is regular for any non-maximal prime ideal $\mathfrak{q}$ then $H^i_P(R)$ has finitely many associate primes for all $i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local cohomology of ideals and the $R_n$ condition of Serre Puthenpurakal, Tony J. Commutative Algebra 13D45 Let $R$ be a regular ring of dimension $d$ containing a field $K$ of characteristic zero. If $E$ is an $R$-module let $Ass^i E = \{ Q \in \ Ass E \mid \ height Q = i \}$. Let $P$ be a prime ideal in $R$ of height $g$. We show that if $R/P$ satisfies Serre's condition $R_i$ then $Ass^{g+i+1}H^{g+1}_P(R)$ is a finite set. As an application of our techniques we prove that if $P$ is a prime ideal in $R$ such that $(R/P)_\mathfrak{q}$ is regular for any non-maximal prime ideal $\mathfrak{q}$ then $H^i_P(R)$ has finitely many associate primes for all $i$. |
| title | Local cohomology of ideals and the $R_n$ condition of Serre |
| topic | Commutative Algebra 13D45 |
| url | https://arxiv.org/abs/2410.18493 |