English

Telescope conjecture for quiver representations over artinian rings

Representation Theory 2025-12-02 v2 Commutative Algebra Rings and Algebras

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.

Keywords

Cite

@article{arxiv.2509.14179,
  title  = {Telescope conjecture for quiver representations over artinian rings},
  author = {Michal Hrbek and Enrico Sabatini},
  journal= {arXiv preprint arXiv:2509.14179},
  year   = {2025}
}

Comments

14 pages

R2 v1 2026-07-01T05:42:21.669Z