Telescope conjecture for quiver representations over artinian rings

Fuente: arXiv
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Hauptverfasser: Hrbek, Michal, Sabatini, Enrico
Format: Preprint
Veröffentlicht: 2025
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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