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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.25010 |
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| _version_ | 1866914228641726464 |
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| author | Gan, Wee Liang Ta, Khoa |
| author_facet | Gan, Wee Liang Ta, Khoa |
| contents | Fix a finite field $\mathbb{F}$. Let $\mathrm{VI}$ be a skeleton of the category of finite dimensional $\mathbb{F}$-vector spaces and injective $\mathbb{F}$-linear maps. We study $\mathrm{VI}^m$-modules over a noetherian commutative ring in the nondescribing characteristic case. We prove that if a finitely generated $\mathrm{VI}^m$-module is generated in degree $\leqslant d$ and related in degree $\leqslant r$, then its regularity is bounded above by a function of $m$, $d$, and $r$. A key ingredient of the proof is a shift theorem for finitely generated $\mathrm{VI}^m$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_25010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounding regularity of $\mathrm{VI}^m$-modules Gan, Wee Liang Ta, Khoa Representation Theory Fix a finite field $\mathbb{F}$. Let $\mathrm{VI}$ be a skeleton of the category of finite dimensional $\mathbb{F}$-vector spaces and injective $\mathbb{F}$-linear maps. We study $\mathrm{VI}^m$-modules over a noetherian commutative ring in the nondescribing characteristic case. We prove that if a finitely generated $\mathrm{VI}^m$-module is generated in degree $\leqslant d$ and related in degree $\leqslant r$, then its regularity is bounded above by a function of $m$, $d$, and $r$. A key ingredient of the proof is a shift theorem for finitely generated $\mathrm{VI}^m$-modules. |
| title | Bounding regularity of $\mathrm{VI}^m$-modules |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2512.25010 |