中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
表示论讨论班
Speaker: 周宇教授 (北京师范大学)
Inviter: 聂思安
Language: Chinese
Title: Extended module categories and general silting complexes
Time & Venue: 2026年5月28日（星期四） 14: 30 - 15: 30 & N818
Abstract: Over the past decade, τ-tilting theory has completed classical tilting theory from multiple perspectives, notably establishing a well-behaved mutation theory and crucial bijections with functorially finite torsion classes and 2-term silting complexes. However, general silting complexes cannot be fully incorporated into this classical module category setting.
To address this issue, we introduce the notion of extended module categories. In this talk, we define this new categorical structure and discuss how it extends classical module-theoretic results. Specifically, we establish the correspondence between general silting complexes and functorially finite positive torsion classes in this extended setting. Furthermore, we explore new homological phenomena distinct from classical module categories, and highlight specific difficulties arising in higher dimensions, such as the fact that several equivalent characterizations of torsion classes in abelian categories no longer hold in higher dimensions.
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