Article
| Title: | Non-finitely generated bigraded local cohomology modules (English) |
| Author: | Rahimi, Ahad |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 669-679 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $\Bbbk $ be a field, and let $S=\Bbbk [x_1, \dots , x_m, y_1, \dots , y_n]$ denote a standard bigraded polynomial ring over $\Bbbk $. Consider $M$, a finitely generated bigraded $S$-module, and set $Q=\langle y_1, \dots , y_n \rangle $. Assume that there exists $\frak p \in {\rm Ass}_S M$ such that ${\rm cd}(Q, S/\frak p)=j>0$. We demonstrate that ${\rm H}^j_{Q}(M)$ is not finitely generated. Furthermore, we explore a more general version of this result. (English) |
| Keyword: | associated prime |
| Keyword: | bigraded module |
| Keyword: | cohomological dimension |
| Keyword: | finiteness dimension |
| Keyword: | maximal depth |
| Keyword: | local cohomology |
| MSC: | 13C15 |
| MSC: | 13D45 |
| MSC: | 16W50 |
| DOI: | 10.21136/CMJ.2025.0389-24 |
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| Date available: | 2025-05-20T11:51:04Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152965 |
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