Stability approach to torsion pairs on abelian categories
Stability approach to torsion pairs on abelian categories
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DOI：
10.1016/j.jalgebra.2023.08.026
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发表时间：
2023-03
影响因子：
0.9
通讯作者：
Ming Chen;Yanan Lin;Shiquan Ruan
中科院分区：
文献类型：
--
作者：
Ming Chen;Yanan Lin;Shiquan Ruan
本文引入了一种局部细化方法来研究阿贝尔范畴上的稳定性数据，并给出了稳定性数据是最优的充要条件。我们将相干轴类的所有最优稳定性数据在某些加权投影曲线上进行了分类，包括经典投影线、光滑椭圆曲线和某些加权投影线。作为应用，我们通过稳定性数据方法得到了这些类别的扭转对的分类。同时，也为任意管类扭转副的分类提供了新的证明。
In this paper we introduce a local-refinement procedure to investigate stability data on an abelian category, and provide a sufficient and necessary condition for a stability data to be finest. We classify all the finest stability data for the categories of coherent sheaves over certain weighted projective curves, including the classical projective line, smooth elliptic curves and certain weighted projective lines. As applications, we obtain a classification of torsion pairs for these categories via stability data approach. As a by-product, a new proof for the classification of torsion pairs in any tube category is also provided.