Telescope conjecture for quiver representations over artinian rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911293442621440 |
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| author | Hrbek, Michal Sabatini, Enrico |
| author_facet | Hrbek, Michal Sabatini, Enrico |
| contents | Let $\mathcal{D}(RC)$ be the derived category of representations of a small category $C$ over a commutative noetherian ring $R$. We study the homotopically smashing t-structures on this category. Specifying our discussion to the stalk categories $Γ_{\mathfrak{p}}\mathcal{D}(RQ)$ for a finite quiver $Q$ and a prime ideal $\mathfrak{p}$ of $R$, we prove the telescope conjecture for the derived category of representations of finite quivers over artinian rings. More generally, we prove the same result also outside of the noetherian context, for representations of finite quivers over commutative perfect rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Telescope conjecture for quiver representations over artinian rings Hrbek, Michal Sabatini, Enrico Representation Theory Commutative Algebra Rings and Algebras Primary: 16E35, 16G20, Secondary: 16G30, 18G80 Let $\mathcal{D}(RC)$ be the derived category of representations of a small category $C$ over a commutative noetherian ring $R$. We study the homotopically smashing t-structures on this category. Specifying our discussion to the stalk categories $Γ_{\mathfrak{p}}\mathcal{D}(RQ)$ for a finite quiver $Q$ and a prime ideal $\mathfrak{p}$ of $R$, we prove the telescope conjecture for the derived category of representations of finite quivers over artinian rings. More generally, we prove the same result also outside of the noetherian context, for representations of finite quivers over commutative perfect rings. |
| title | Telescope conjecture for quiver representations over artinian rings |
| topic | Representation Theory Commutative Algebra Rings and Algebras Primary: 16E35, 16G20, Secondary: 16G30, 18G80 |
| url | https://arxiv.org/abs/2509.14179 |