汇报标题 (Title)：Stability approach to torsion pairs on abelian categories（阿贝尔领域上的挠对的不变步骤）
汇报人 (Speaker)：阮诗佺 副教授（厦门大学）
汇报功夫 (Time)：2023年7月9日(周日) 16:00
汇报地址 (Place)：校本部F427
约请人(Inviter)：高楠 教授
主办部门：理学院数学系
汇报提要：The stability data on an abelian category has a close relation with torsion theory. In this report 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. This is joint work with Mingfa Chen and Yanan Lin.
