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arXiv · 2503.11184

A characterization of 2-fold torsion classes induced by $\tau$-rigid modules

Yuki Uchida
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Abstract

We introduce $n$-fold torsion(-free) classes of an abelian category. These are a generalization of ordinary torsion(-free) classes in the sense that $1$-fold torsion(-free) classes coincide with torsion(-free) classes. In the category of finitely generated modules over a finite dimensional algebra, we can naturally construct $n$-fold torsion classes from $\tau$-rigid modules. We characterize the $2$-fold torsion classes induced by $\tau$-rigid modules.

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BibTeXRIS

Yuki Uchida. 2025-03-14. A characterization of 2-fold torsion classes induced by $\tau$-rigid modules. https://arxiv.org/abs/2503.11184

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