报 告 人：周国栋 教授
报告题目：Relative derived categories, relative singularity categories and relative defect categories
报告时间：2021年06月05日 下午16：00-17：00
报告地点：静远楼1508学术报告厅
主办单位：数学与统计学院、科学技术研究院
报告人简介：
周国栋，华东师范大学教授、博士生导师，上海市浦江人才计划获得者。主要从事代数表示论和同调代数等领域研究工作。在Trans. Amer. Math. Soc., J. London Math Soc., Math. Z., Pacific J. Math., J.Algebra，J. Pure Appl Algebra等国际数学期刊发表论文20余篇。主持国家自然科学基金项目3项。
报告摘要：
We introduce the relative Gorenstein defect category of an abelian category with respect to an admissible subcategory, generalizing Gorenstein defect categories of P. A. Bergh, D. Jorgensen and S. Oppermann. Under a mild condition of precovering property for the relative Gorenstein category, we show that the relative Gorenstein defect category is triangle equivalent to the relative singularity category with respect to the relative Gorenstein category.We also introduce relative Ding projective defect categories and under a similar condition, relate it to the relative singularity category with respect to the relative Ding projective category. Analogous results for relative Ding injective defect categories are also presented.We reprove and extend many results in the literature.