Asymptotic Properties of Filtrations of Ideals
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909995673583616 |
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| author | Nasernejad, Mehrdad Toledo, Jonathan |
| author_facet | Nasernejad, Mehrdad Toledo, Jonathan |
| contents | We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration $\mathcal{F} = \{I_i\}_{i \in \mathbb{N}}$, we define $\mathcal{F}$-persistence and $\mathcal{F}$-strong persistence, extending the classical notions for ordinary and symbolic powers of ideals. We show that if $\mathcal{F}$ is strongly persistent, then $\mathcal{F}_{\mathrm{sym}}$ is strongly persistent, where $\mathcal{F}_{\mathrm{sym}}$ denotes the symbolic filtration associated with the filtration $\mathcal{F}$. In addition, we prove that if $\mathcal{F}$ is strongly persistent, then $\mathcal{F}$ is persistent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Properties of Filtrations of Ideals Nasernejad, Mehrdad Toledo, Jonathan Commutative Algebra We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration $\mathcal{F} = \{I_i\}_{i \in \mathbb{N}}$, we define $\mathcal{F}$-persistence and $\mathcal{F}$-strong persistence, extending the classical notions for ordinary and symbolic powers of ideals. We show that if $\mathcal{F}$ is strongly persistent, then $\mathcal{F}_{\mathrm{sym}}$ is strongly persistent, where $\mathcal{F}_{\mathrm{sym}}$ denotes the symbolic filtration associated with the filtration $\mathcal{F}$. In addition, we prove that if $\mathcal{F}$ is strongly persistent, then $\mathcal{F}$ is persistent. |
| title | Asymptotic Properties of Filtrations of Ideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2601.13794 |