(Generalized) Generating Hypothesis in t-Categories

发布时间：2025-04-16 作者：浏览次数：

Speaker:	扶先辉	DateTime:	2025年4月20日（周日）下午15:20-16:20
Brief Introduction to Speaker: 扶先辉，东北师范大学数学与统计学院副院长、教授、博士生导师。研究领域为同调代数和K-理论，现致力于逼近理论及其相关课题的研究，研究工作发表于Adv. Math., Proc. London Math. Soc., J. Algebra, J. Pure Appl. Algebra等期刊。多次主持国家自然科学基金项目，并曾在第十三届全国代数学学术会议和第八届中日韩国际环论会议做大会报告。		Place:	国交2号楼315会议室
Abstract:Suppose D is a t-category whose heart is denoted as A . A morphism f in D is said to be a ghost morphism provided that H^n(f)=0 for all n in Z, where H^n(-) is the cohomology functor induced by the t-structure D. In this talk, I will prove a version of the n-fold Generalized Generating Hypothesis: If D is non-degenerate and countably cocomplete such that A has enough projective objects and every Yoneda extension group YExt^q_A(M,N) is canonically isomorphic to Hom_D(M, N[q]), then proj.dim A+1 is precisely the supremum of how many concatenating ghost morphisms can compose non-trivially. I will give a very detailed analysis of the cases where n=1 and 2, which have very interesting relations with semisimple and hereditary triangulated categories. As an application, we will study the famous n-fold Generating Hypothesis under the circumstances where our t-category is generated by a rigid compact generator G. We will demonstrate that, under some reasonable assumptions, the t-structure in...

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