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Telescope conjecture for quiver representations over artinian rings

Published 17 Sep 2025 in math.RT, math.AC, and math.RA | (2509.14179v1)

Abstract: Let D(RC)\mathcal{D}(RC) be the derived category of representations of a small category CC over a commutative noetherian ring RR. We study the homotopically smashing t-structures on this category. Specifying our discussion to the stalk categories ΓpD(RQ)\Gamma_{\mathfrak{p}}\mathcal{D}(RQ) for a finite quiver QQ and a prime ideal p\mathfrak{p} of RR, 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.

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