报告题目：Model Structures Arising from Weak Cotorsion Pairs
报告人： Ramin Ebrahimi 博士
主持人： Rasool Hafezi 副教授
报告时间：2026年10月16日（周五）15：30-16：30
报告地点：藕舫楼702室
报告摘要：Let A be an abelian category. Hovey [1] established a bijective correspondence between admissible model structures on A and certain compatible pairs of cotorsion pairs. Subsequently, Beligiannis and Reiten [2] showed that projective model structures can be parametrized by a single hereditary cotorsion pair with a contravariantly finite core. Their correspondence also provides a homotopical interpretation of classical tilting theory. Support τ -tilting theory, introduced by Adachi, Iyama and Reiten [3], is an important generalization of classical tilting theory. While tilting modules induce cotorsion pairs, support τ -tilting modules are naturally related to left weak cotorsion pairs, as investigated by Buan and Zhou [4]. In this talk, we introduce the notion of a weak projective model structure and establish a bijective correspondence between weak projective model structures and hereditary left weak cotorsion pairs with contravariantly finite cores. This generalizes the Beligiannis–Reiten correspondence. As an application, we show that every support τ -tilting module over an Artin algebra induces a model structure. Moreover, we obtain a bijective correspondence between isoclasses of basic support τ -tilting modules and weak projective model structures whose subcategories of trivially fibrant objects are closed under factor modules.
报告人简介：Ramin Ebrahimi is a postdoc in Zhejiaing Normal University. He received his PhD in mathematics in 2020 in the universityof Isfahan, under supervision of Dr Alireza Nasr-Isfahani. His research field concernsthe representation theory of algebras, homological algebra and derived categories. He has some research papers in some prestigious journals such as International Mathematics Research Notices, Bulletin of London Mathematical Society, The Quarterly Journal of Mathematics and Journal of Algebra.
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数学与统计学院
江苏省应用数学（南京信息工程大学）中心
江苏省系统建模与数据分析国际合作联合实验室
2026年10月15日
