Telescope Conjecture for t-Structures: Quiver Representations over Commutative Noetherian Rings

This thesis establishes affirmative results on the telescope conjecture for t-structures in the derived category of quiver representations over commutative noetherian rings. After outlining the general context, we proceed by introducing certain restrictions either on the class of commutative rings or on the type of quivers considered. Specifically, we prove the telescope conjecture for t-structures in the derived category of representations of finite quivers over commutative artinian rings, and in the derived category of representations of Dynkin quivers over commutative noetherian rings. Finally, to address the problem in greater generality, we consider the derived category of representations of finite, acyclic quivers over commutative noetherian rings equipped with a tensor triangulated structure. In this setting, we prove that the telescope conjecture holds for tensor-compatible t-structures.