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arXiv · 2511.20204

The Balmer spectrum and tensor telescope conjecture for noetherian path algebras

Enrico Sabatini
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Abstract

Given a commutative noetherian ring $R$ and a finite acyclic quiver $Q$, we study the tensor triangulated category $\mathcal{D}(RQ)$ endowed with the vertexwise tensor product. We find a description of the internal hom functor and show that the category is not rigid. We compute its Balmer spectrum and, despite the non-rigidity, we get a classification of all the thick tensor-ideals and a stratification result. After introducing the notion of tensor-t-structure, we give a classification of the compactly generated ones and prove the tensor telescope conjecture.

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Enrico Sabatini. 2025-11-29. The Balmer spectrum and tensor telescope conjecture for noetherian path algebras. https://arxiv.org/abs/2511.20204

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