Koszul cohomology and support of local cohomology modules of complete intersections
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912609712734208 |
|---|---|
| author | Gintz, Michael Zhang, Wenliang |
| author_facet | Gintz, Michael Zhang, Wenliang |
| contents | Let $R$ be a noetherian commutative ring and $f_1,\dots,f_c$ be a regular sequence in $R$. We introduce a framework to study $Supp(H^j_I(R/(f_1,\dots,f_c)))$ by linking the Koszul cohomology of $H^j_I(R)$ on the sequence $f_1,\dots,f_c$ and local cohomology modules $H^j_I(R/(f_1,\dots,f_c))$. As an application, we prove that if $R$ is a noetherian regular ring of prime characteristic $p$ and $f_1,f_2$ form a regular sequence in $R$ then $Supp(H^j_I(R/(f_1,f_2)))$ is Zariski-closed for each integer $j$ and each ideal $I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Koszul cohomology and support of local cohomology modules of complete intersections Gintz, Michael Zhang, Wenliang Commutative Algebra Let $R$ be a noetherian commutative ring and $f_1,\dots,f_c$ be a regular sequence in $R$. We introduce a framework to study $Supp(H^j_I(R/(f_1,\dots,f_c)))$ by linking the Koszul cohomology of $H^j_I(R)$ on the sequence $f_1,\dots,f_c$ and local cohomology modules $H^j_I(R/(f_1,\dots,f_c))$. As an application, we prove that if $R$ is a noetherian regular ring of prime characteristic $p$ and $f_1,f_2$ form a regular sequence in $R$ then $Supp(H^j_I(R/(f_1,f_2)))$ is Zariski-closed for each integer $j$ and each ideal $I$. |
| title | Koszul cohomology and support of local cohomology modules of complete intersections |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2509.22988 |